F.IF.1. SELECTED RESPONSE Select the correct answer. 1. What are the domain and range of the function y = f (x) as shown on the graph?

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1 Name Date Class F.IF.1 SELECTED RESPONSE Select the correct answer. 1. What are the domain and range of the function y = f (x) as shown on the graph? The domain is {0.25, 0.5,1, 2, 4, 8}, and the range is { 3, 2, 1, 0, 1, 2}. The domain is { 3, 2, 1, 0, 1, 2} and the range is {0.25, 0.5,1, 2, 4, 8}. The domain is all real numbers between 3 and 2, and the range is all real numbers between 0.25 and 8. The domain is all real numbers between 0.25 and 8, and the range is all real numbers between 3 and The linear function f (x) has the domain x 5. Which of the following does not represent an element of the range? f f (5) f ( ) f (100,000) Select all correct answers. 3. The domain of the function f(x) is the set of integers greater than 5. Which of the following values represent elements of the range of f? 1 f (4.8) f 2 f ( 2) f (0) f ( 5) f (14) f (8) f ( 18) CONSTRUCTED RESPONSE 4. Examine the two sets below. The first is the set of months in the year and the second is the possible numbers of days per month. Is the relation that maps the month to its possible number of days a function? Explain. Algebra 1 57 Common Core Assessment Readiness

2 Name Date Class 5. Does the table represent a function? If so, state the domain and range. If not, state why. x f(x) An exponential function y = f(x) is graphed below. The graph has a horizontal asymptote at y = 3. What are the domain and range of f(x)? 6. The graph of y = 1 x + 3 is shown 2 below. Use the graph to find the y-values associated with x = 2, x = 0, and x = 2. If y = f(x) is a function, which of the values given above are in the range and which are in the domain? 8. Determine whether the following situations represent functions. Explain your reasoning. If the situation represents a function, give the domain and range. a. Each U.S. coin is mapped to its monetary value. b. A $1, $5, $10, $20, $50, or $100 bill is mapped to all the sets of coins that are the same total value as the bill. Algebra 1 58 Common Core Assessment Readiness

3 Name Date Class F.IF.2 SELECTED RESPONSE Select the correct answer. 1. What is the value of the function f(x) = x 2 5x + 2 evaluated at x = 2? Joshua is driving to the store. The average distance d, in miles, he travels over t minutes is given by the function d(t) = 0.5t. What is the value of the function when t = 15? 75 miles 7.5 minutes 7.5 miles 15 minutes 3. Marcello is tiling his kitchen floor with 45 square tiles. The tiles come in wholenumber side lengths of 6 to 12 inches. The function A(s) = 45s 2, where s is the side length of the tile, represents the area that Marcello can cover with the tiles. What is the domain of this function? All real numbers between 6 and 12, inclusive All rational numbers between 6 and 12, inclusive {6, 7, 8, 9, 10, 11, 12} {6, 12} Select all correct answers. 4. Which values are in the domain of the function f(x) = 6x + 11 with a range { 37, 25, 13, 1}? CONSTRUCTED RESPONSE 5. The production cost for g graphing calculators is C(g) = 25g. Evaluate the function at g = 15. What does the value of the function at g = 15 represent? 6. The domain of the function f(x) = 13x x 2 is given as { 2, 1, 0, 1, 2}. What is the range? Show your work. Algebra 1 59 Common Core Assessment Readiness

4 Name Date Class 7. Victor needs to find the volume of cubeshaped containers with side lengths ranging from 2 feet to 7 feet. The side lengths of the containers can only be whole numbers. The volume of a container with side length s is given by V(s) = s 3. a. What is the domain of the function? b. Evaluate the function at each value in the domain. Show your work. 8. A store selling televisions is calculating the profit for one model. Currently, the store has 25 televisions in stock. The store bought these televisions from a supplier for $99.50 each. Each television will be sold for $ a. Write a profit function in terms of n, the number of televisions sold. b. What is the domain of the function? Explain. c. If the store sold all of the televisions in stock, how much would the profit be? 9. Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets p left after t minutes of printing is given by the function p(t) = 8t a. How long would it take the printer to use all 100 sheets of paper? Explain how you found your answer. b. What is the domain of the function? Explain. c. What is the range of the function? Explain. d. Tanya s report takes 7 minutes to print. How long is Tanya s report? Show your work. Algebra 1 60 Common Core Assessment Readiness

5 Name Date Class F.IF.3 SELECTED RESPONSE Select the correct answer. 1. Which function below generates the sequence 2, 0, 2, 4, 6,? f(n) = n 2, where n 0 and n is an integer. f(n) = 2n 2, where n 0 and n is an integer. f(n) = 2n + 2, where n 1 and n is an integer. f(n) = 2n, where n 0 and n is an integer. 2. The sequence 1, 2, 7, 14, can be generated by the function f(n) = n 2 2. What is the domain of the function? The domain is the set of all positive real numbers. The domain is the set of all real numbers greater than 1. The domain is the set of integers n such that n 0. The domain is the set of integers n such that n 1. Select all correct answers. 3. Which of the functions below could be used to generate the sequence 1, 2, 4, 8, 16, 32,? f(n) = 2 n, where n 0 and n is an integer. f(n) = 2 n, where n 1 and n is an integer. f(1) = 1, f(n) = 2(f(n 1)), where n 2 and n is an integer. f(n) = 2(n 1), where n 1 and n is an integer. f(n) = n 2, where n 1 and n is an integer. Match each sequence with a function that generates it. 4. 4, 12, 24, 40, 60, A f(n) = 3n, n 1 and n is an integer. 5. 0, 1 2, 2 3, 3 4, 4 5, B f(n) = 2n(n + 1), n 1 and n is an integer , 24, 12, 6, 3, C f(n) = 2(n + 2), n 0 and n is an integer. 7. 3, 6, 9, 12, 15, D f (n) = n 1, n 1 and n is an integer. n 8. 3, 6, 11, 18, 27, E f(n) = n 2 + 2, n 1 and n is an integer. F f(1) = 48 and f (n) = 1 f (n 1), n 2 and n is an integer. 2 G f(1) = 48 and f(n) = 2f(n 1), n 2 and n is an integer. H f (n) = n, n 1 and n is an integer. n +1 Algebra 1 61 Common Core Assessment Readiness

6 Name Date Class CONSTRUCTED RESPONSE 9. Consider the sequence 1, 2, 5, 10, 17, a. Write a quadratic function f(n) that generates the sequence. Assume that the domain of the function is the set of integers n 0. b. Use your result from part a to determine the 15th term of the sequence. 10. The domain of a function f defining the sequence 2 3, 3 4, 4 5, 5 6, 6, is the set of 7 consecutive integers starting with 1. a. What is f(3)? Explain. b. How does your answer to part a change if the domain of the function is the set of consecutive integers starting with 0? 11. The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, a. Write a recursive function to describe the terms of the Fibonacci sequence. Begin with the conditions f(0) = f(1) = 1 and f(2) = f(1) + f(0). b. Suppose the first two terms of the Fibonacci sequence were f(0) = 2 and f(1) = 2, instead of f(0) = 1 and f(1) = 1. Write the first 5 terms of the sequence. c. Explain how you can modify your answer from part a to describe the terms of the sequence found in part b. 12. Consider the sequence 1, 3, 5, 7, 9, a. Write a function describing the sequence whose domain is the set of consecutive integers starting with 1. b. Write a recursive function describing the sequence. Algebra 1 62 Common Core Assessment Readiness

7 Name Date Class F.IF.4* SELECTED RESPONSE Select the correct answer. 1. The graph shows the height h(t) of a model rocket t seconds after it is launched from the ground at 48 feet per second. Where is the height of the rocket increasing? Where is it decreasing? Select all correct answers. 2. Choose all the statements that are true about the graph. The height of the rocket is always increasing. The height of the rocket is always decreasing. The height of the rocket is increasing when 0 < t < 3 and decreasing when 3 < t < 6. The height of the rocket is increasing when 3 < t < 6 and decreasing when 0 < t < 3. The x-intercept is 9. The y-intercept is 2. f(x) is increasing when x < 1. f(x) is decreasing when x > 1. f(x) has a local maximum at (1, 2). f(x) has a local minimum at (1, 2). f(x) is negative when x < 9. f(x) is positive when x > 2. CONSTRUCTED RESPONSE 3. Martha s text message plan costs $15.00 for the first 1000 text messages sent plus $0.25 per text over 1000 sent. Let C(t) represent the cost of sending t text messages over Sketch a graph of this relationship, and find and interpret the C(t) -intercept. Algebra 1 63 Common Core Assessment Readiness

8 Name Date Class 4. The profit produced by an apple orchard increases as more trees are planted. However, if the orchard becomes overcrowded, the trees will start to produce fewer apples, and the profit will start to decrease. The owner of a small apple orchard recorded the following approximate profit values P(a) in the table below, where a is the number of apple trees in the orchard. Using the data in the table, identify where P(a) is increasing and decreasing. Find when the owner earned the least profit and when the owner earned the most profit. a P(a) The absolute value function y = x can be described using the following piecewise function. f (x) = x, x < 0 x, 0 x a. Graph f(x). b. Where is the function decreasing and increasing? c. Where is f(x) positive? d. Explain why f(x) is never negative. Algebra 1 64 Common Core Assessment Readiness

9 Name Date Class F.IF.5* SELECTED RESPONSE Select the correct answer. 1. The function h(n) gives the number of person-hours it takes to assemble n engines in a factory. What is a reasonable domain for h(n)? The nonnegative rational numbers The real numbers The nonnegative integers The nonnegative real numbers 3. The growth of a population of bacteria can be modeled by an exponential function. The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks, that has passed. The initial population of the bacteria colony was 500. What is the domain of the function? What does the domain represent in this context? 2. The graph of the quadratic function f(x) is shown below. What is the domain of f(x)? The integers greater than 3. The real numbers greater than 3. The integers The real numbers The domain is the real numbers greater than 500. The domain represents the time, in weeks, that has passed. The domain is the real numbers greater than 500. The domain represents the population of the colony after a given number of weeks. The domain is the nonnegative real numbers. The domain represents the time, in weeks, that has passed. The domain is the nonnegative real numbers. The domain represents the population of the colony after a given number of weeks. Algebra 1 65 Common Core Assessment Readiness

10 Name Date Class CONSTRUCTED RESPONSE 4. The function h(t) describes the height, in feet, of an object at time t, in seconds, when it is launched upward from the ground at an initial speed of 112 feet per second. 6. An electronics store sells a certain brand of tablet computer for $500. To stock the tablet computers, the store pays $150 per unit. The store also spends $1800 setting up a special display area to promote the product. a. Write a function rule to describe the profit earned from selling the tablet computers. Note that profit is the revenue earned minus the cost. b. What is a reasonable domain for the function? Explain. a. Find the domain. b. What does the domain mean in this context? 5. What are the domain and range of the exponential function f(x)? c. What are the first eight values in the range of the function? (Start with the range value that corresponds to the least value in the domain.) 7. A grocery store sells two brands of ham by the pound. Brand A costs $4.19 per pound, and brand B costs $4.79 per pound. Brand A can be purchased at the deli in any amount, whereas brand B comes in prepackaged containers of either 0.5 pound or 1 pound. Write a function rule that represents the revenue earned for each of the brands and determine a reasonable domain for each. Explain your answers. Algebra 1 66 Common Core Assessment Readiness

11 Name Date Class F.IF.6* SELECTED RESPONSE Select the correct answer. 1. The table shows the height of a sassafras tree at each of two ages. What was the tree s average rate of growth during this time period? Age (years) Height (meters) meter per year 0.5 meter per year 2 meters per year 2.5 meters per year 2. The graph shows the height h, in feet, of a football at time t, in seconds, from the moment it was kicked at ground level. Estimate the average rate of change in height from t = 1.5 seconds to t = 1.75 seconds. 20 feet per second 12 feet per second 12 feet per second 20 feet per second 3. Find the average rate of change of the function f (x) = 2 x from x = 9 to x = Select all correct answers. 4. A person s body mass index (BMI) is calculated by dividing the person s mass in kilograms by the person s height in meters. The table shows the median BMI for U.S. males from age 2 to age 12. For which intervals is the average rate of change in the BMI positive? Age (years) Median BMI age 2 to age 4 age 4 to age 6 age 6 to age 8 age 8 to age 10 age 10 to age 12 Select the correct answer for each lettered part. 5. Determine whether each function s average rate of change on the interval x = 0 to x = 2 is equal to 2. a. f(x) = x + 2 Yes No b. f(x) = 2x Yes No c. f (x) = x Yes No d. f(x) = x 2 Yes No e. f(x) = 2 x Yes No Algebra 1 67 Common Core Assessment Readiness

12 Name Date Class CONSTRUCTED RESPONSE 6. The table gives the minutes of daylight on the first and last day of October 2012 for Anchorage, Alaska, and Los Angeles, California. Location Daylight on Oct. 1 Anchorage Los Angeles Daylight on Oct. 31 a. Calculate the average rate of change, in minutes per day, of daylight during October for each location. 7. The graph models the population P(t) of a bacteria colony as a function of time t, in weeks. b. Interpret your answers from part a. In other words, how are the day lengths changing in Anchorage and Los Angeles in October? c. The sun rises at 7:00 A.M. on October 17, 2012, in Los Angeles. Estimate the time at which the sun sets that day. Explain your reasoning and show your work. a. Determine the average growth rate between weeks 2 and 3. b. Determine the average growth rate between weeks 3 and 4. c. Determine the average growth rate between weeks 4 and 5. d. What is happening to the average growth rate as each week passes? Justify your answer. e. What do you think the average growth rate will be between weeks 5 and 6 if the pattern continues? Algebra 1 68 Common Core Assessment Readiness

13 Name Date Class F.IF.7a* SELECTED RESPONSE Select the correct answer. 1. What are the intercepts of the linear function shown? CONSTRUCTED RESPONSE 3. Sally decides to make and sell necklaces to earn money to buy a new computer. She plans to charge $5.25 per necklace. a. Write a function that describes the revenue R(n), in dollars, Sally will earn from selling n necklaces. b. What is a reasonable domain for this function? x-intercept: 2; y-intercept: 2 x-intercept: 2; y-intercept: 4 x-intercept: 2; y-intercept: 4 x-intercept: 2; y-intercept: 4 c. Graph the function. 2. What is the vertex of the quadratic function f(x)? Is it a maximum or a minimum? d. Identify and interpret the intercepts of the function. (1, 4); minimum (0, 3); minimum ( 1, 0); minimum (3, 0); maximum Algebra 1 69 Common Core Assessment Readiness

14 Name Date Class 4. The function h(t) = 4.9t t models the height h(t), in meters, of an object t seconds after it is thrown upward from the ground with an initial velocity of 24.5 meters per second. a. Calculate and interpret the intercepts of the function. b. Calculate the vertex of the function. 5. A farmer has 1200 feet of fencing to enclose a square area for his horses and a rectangular area for his pigs. The farmer decides that the enclosures should share a full side to maximize the usefulness of the fencing. He also wants to maximize the combined area of the enclosures. Write a function that describes the combined area of the enclosures A(s) as a function of the side length s of the square enclosure. Then, graph the function to determine dimensions of each enclosure that maximize the combined area. Explain your answer. c. Is the vertex a minimum or a maximum? What does this mean in this context? d. Plot the points found in parts a and b and then graph the function. Algebra 1 70 Common Core Assessment Readiness

15 Name Date Class F.IF.7b* SELECTED RESPONSE Select the correct answer. 1. What kind of function best describes the following graph? 3. What is the vertex of f(x)? Is it a maximum or a minimum? An absolute value function A cube root function A square root function A step function 2. What are the x- and y-intercept(s) of f(x)? (0, 2); minimum (3, 5); minimum ( 2, 0); minimum (8, 0); maximum CONSTRUCTED RESPONSE 4. Graph the piecewise defined function. What are the domain and range? 2 x < 3 f (x) = 1 3 x < 1 4 x 1 x-intercept: 1 y-intercept: 1 x-intercept: 5; y-intercept: 1 x-intercepts: 5, 1; y-intercept: 1 Algebra 1 71 Common Core Assessment Readiness

16 Name Date Class 5. A simple reaction time test involves dropping a meter-long ruler between someone s thumb and index finger and measuring the time it takes for the person to catch it against the distance the ruler travels. The function t(d) = d models the approximate reaction time t(d), in seconds, as a function of the distance d the ruler travels, in centimeters. Graph the function. What happens to the reaction time as the distance increases? Explain your answer by interpreting the graph. 6. Write and graph a piecewise-defined step function f(x) that has the following characteristics. I. f(x) has more than one x-intercept II. The domain of f(x) is the real numbers III. The range of f(x) consists of four unique integers 3 7. Graph the function f (x) = 2 x Find the intervals where the function is increasing and decreasing. Algebra 1 72 Common Core Assessment Readiness

17 Name Date Class F.IF.7e* SELECTED RESPONSE Select the correct answer. 1. The exponential function f(x) has a horizontal asymptote at y = 3. What is the end behavior of f(x)? 2. A website allows its users to submit and edit content in an online encyclopedia. The graph shows the number of articles a(t) in the encyclopedia t months after the website goes live. How many articles were in the encyclopedia when it went live? As x decreases without bound, f(x) decreases without bound. As x increases without bound, f(x) increases without bound. As x decreases without bound, f(x) increases without bound. As x increases without bound, f(x) decreases without bound. As x decreases without bound, f(x) approaches, but never reaches, 3. As x increases without bound, f(x) increases without bound. As x decreases without bound, f(x) decreases without bound. As x increases without bound, f(x) approaches, but never reaches, Select all correct answers. 3. Which statements are true about the graph of the exponential function f(x)? The domain is all real numbers. The range is all real numbers. The f(x)-intercept is 3. The x-intercept is 1. As x increases without bound, f(x) approaches, but never reaches, 1. Algebra 1 73 Common Core Assessment Readiness

18 Name Date Class CONSTRUCTED RESPONSE 4. Suppose an exponential function has a domain of all real numbers and a range that is bounded by an integer. How many x-intercepts could such a function have? Graph examples to support your answer. 5. The value of an object decreases from its purchase price over time. This change in value can be modeled using an exponential function. A new copy machine purchased by a school for $1200 has an estimated useful life span of 12 years. After 12 years, the copier is worth $250. The value V(t) of the copier after t years is approximated by the function V(t) = 1200(0.88) t. a. Graph the function on the domain 0 t 12. b. Estimate and interpret the V(t)-intercept. Algebra 1 74 Common Core Assessment Readiness

19 Name Date Class F.IF.8a SELECTED RESPONSE Select the correct answer. 1. What are the zeros of the function f(x) = x 2 + 2x 8? x = 4 and x = 2 x = 4 and x = 2 x = 4 and x = 2 x = 4 and x = 2 2. What is the axis of symmetry of the graph of f(x) = 3x 2 6x + 6? x = 1 x = 1 y = 1 y = 3 Select all correct answers. 3. Which of the following statements correctly describe the graph of f(x) = 2x 2 + 8x 2? The maximum value of the function is 10. The minimum value of the function is 10. The axis of symmetry is the line x = 2. The axis of symmetry is the line x = 2. The graph is a parabola that opens up. The graph is a parabola that opens down. Select the correct answer for each lettered part. 4. Consider the function f(x) = 2x 2 + 4x 30. Classify each statement. a. The vertex of the graph of f(x) is (1, 32). True False b. The zeros of f(x) are x = 3 and x = 5. True False c. The graph of f(x) opens down. True False d. The axis of symmetry is x = 1. True False e. The y-intercept of f(x) is 30. True False CONSTRUCTED RESPONSE 5. Consider the function f(x) = 4x 2 + 4x 15. a. Factor the expression 4x 2 + 4x 15. What are the zeros of f(x)? b. What are the coordinates of the vertex of f(x)? Is the vertex the maximum or minimum value of the function? Explain. Algebra 1 75 Common Core Assessment Readiness

20 Name Date Class 6. The axis of symmetry for a quadratic function is a vertical line halfway between the x-intercepts of the function. Miguel says that the graph of f(x) = 2x 2 16x 34 has no axis of symmetry because the function has no x-intercepts. a. Explain why Miguel is incorrect. b. Find the axis of symmetry of the graph of f(x). Show your work. 7. The arch that supports a bridge that passes over a river forms a parabola whose height above the water level is given by h(x) = x2 + 45, where x = 0 represents the center of the bridge. The distance between the sides of the arch at the water level is the same as the length of the bridge. a. How long is the bridge? Explain. b. A sailboat with a mast that extends 50 feet above the water is sailing down the river. Will the sailboat be able to pass under the bridge? Explain. Algebra 1 76 Common Core Assessment Readiness

21 Name Date Class F.IF.8b SELECTED RESPONSE Select the correct answer. 1. The balance B, in dollars, after t years of an investment that earns interest compounded annually is given by the function B(t) = 1500(1.045) t. To the nearest hundredth of a percent, what is the monthly interest rate for the investment? 0.37% 4.50% 3.67% 69.59% 2. After t days, the mass m, in grams, of 100 grams of a certain radioactive element is given by the function m(t) = 100(0.97) t. To the nearest percent, what is the weekly decay rate of the element? 3% 21% 19% 81% Select all correct answers. 3. Which of these functions describe exponential growth? f(t) = 1.25 t f(t) = 2(0.93) 0.5t f(t) = 3(1.07) 3t f(t) = 18(0.85) t f(t) = 0.5(1.05) t f(t) = 3(1.71) 5t f(t) = t f(t) = 8(1.56) 1.4t Select the correct answer for each lettered part. 4. Determine if each function below is equivalent to f(t) = 0.25 t. t a. f (t) = 14 Equivalent Not equivalent b. f (t) = t Equivalent Not equivalent t c. f (t) = Equivalent Not equivalent t d. f (t) = Equivalent Not equivalent e. f (t) = 4 t Equivalent Not equivalent f. f (t) = t Equivalent Not equivalent CONSTRUCTED RESPONSE 5. The population P, in millions, of a certain country can be modeled by the function P(t) = 3.98(1.02) t, where t is the number of years after a. Write the equation in the form P(t) = a(1 + r) t. b. What is the value of r in your answer from part a? What does this value represent? Algebra 1 77 Common Core Assessment Readiness

22 Name Date Class 6. How do the function values of g(x) = 200(4 x 1 ) compare to the corresponding function values of f(x) = 200(4 x )? Explain using a transformation of g(x). 7. The value V, in dollars, after t years of an investment that earns interest compounded annually is given by the function V(t) = 1500(1.035) t. a. Rewrite V(t) to find the annual interest rate of the investment. b. Find the approximate interest rate over a 5-year period by rewriting the function using the power of a power property. Round to the nearest percent. 8. Sanjay plans to deposit $850 in a bank account whose balance B, in dollars, after t years is modeled by B(t) = 850(1.04) t. a. Write the equation in the form B(t) = a(1 + r) t. What is the annual interest rate of Sanjay s account? b. Rewrite the equation from part a to approximate the monthly interest rate. Round to the nearest hundredth of a percent. c. Rebecca deposits $850 in a bank account that earns 0.35% interest compounded monthly. Without calculating the account balances, which account will have a larger balance after 6 months? Explain. Algebra 1 78 Common Core Assessment Readiness

23 Name Date Class F.IF.9 SELECTED RESPONSE Select the correct answer. 1. A quadratic function is shown below. Which function has the same domain? Select all correct answers. 3. Which functions have the same range as the cube root function f(x) shown in the graph? f (x) = x 2 g(x) = x 2 h(x) = x 2 k(x) = 3 x, x 2 2. The function f(x) is defined for only the values given in the table. Which function has the same x-intercepts as f(x)? x f(x) g(x) = 2x + 2 h(x) = 1 3 x + 2 j(x) = x 2 + 2x 3 k(x) = x 1 2 g(x) = x + 2 h(x) = 1 3 x +1 j(x) = x 2 6x + 8 k(x) = 2x 1 m(x) = 3 2x 1+ 2 CONSTRUCTED RESPONSE 4. The function f(x) is defined for only the values in the table. Let g(x) = x for all real numbers 1 x 4. Compare the domains, ranges, and initial values of the functions. x f(x) Algebra 1 79 Common Core Assessment Readiness

24 Name Date Class 5. Which of the functions described below has a greater maximum value on the domain 6 x 6? Explain. x g(x) x g(x) A company offers two cell phone plans to its employees. The function A(t) = 70t gives the cost, in dollars, of cell phone plan A for t months. Plan B allows an employee to receive an additional discount by paying for a certain number of months in advance. The table describes the function B(t), which gives the cost, in dollars, of cell phone plan B for t months. t B(t) 1 $70 2 $140 3 $200 4 $250 5 $290 6 $330 a. Which plan costs more for 3 months? Explain. b. After how many months will an employee on plan B be saving more than $50 over an employee on plan A? Explain. Algebra 1 80 Common Core Assessment Readiness

25 Name Date Class F.BF.1a* SELECTED RESPONSE Select the correct answer. 1. A small swimming pool initially contains 400 gallons of water, and water is being added at a rate of 10 gallons per minute. Which expression represents the volume of the pool after t minutes? 10t t t (1.10) t 2. A diver jumps off a 10-meter-high diving board with an initial vertical velocity of 3 meters per second. The function h(t) = 4.9t 2 + v 0 t + h 0 models the height of a falling object, where v 0 is the initial vertical velocity and h 0 is the initial height. Which function models the divers height h, in meters, above the water at time t, in seconds? h(t) = 4.9t 2 3t + 10 h(t) = 4.9t 2 3t 10 h(t) = 4.9t 2 + 3t + 10 h(t) = 4.9t 2 + 3t Andrea buys a car for $16,000. The car loses value at a rate of 8% each year. Which recursive rule below describes the value of Andrea s car V, in dollars, after t years? V(0) = $16,000 and V(t) = 0.08 i V(t 1) for t 1 V(0) = $16,000 and V(t) = 0.2 i V(t 1) for t 1 V(0) = $16,000 and V(t) = 0.92 i V(t 1) for t 1 V(0) = $16,000 and V(t) = 1.08 i V(t 1) for t 1 Select all correct answers. 4. Miguel has $250 dollars saved, and he adds $5 to his savings every week. Which functions describe the amount A, in dollars, that Miguel has saved after t weeks? A(t) = 5t A(t) = 5t A(t) = 250t + 5 A(0) = 250 and A(t) = A(t 1) + 5 for t 1 A(0) = 250 and A(t + 1) = A(t) + 5 for t 0 A(0) = 250 and A(t + 1) = 5A(t) for t 0 CONSTRUCTED RESPONSE 5. When a piece of paper is folded in half, the total thickness doubles and the total area is halved. Suppose you have a sheet of paper that is 0.1 mm thick and has an area of 10,000 mm 2. a. Write an equation that models the thickness T, in millimeters, of the sheet of paper after it has been folded n times. b. Write an equation that models the area A, in square millimeters, of the sheet of paper after it has been folded n times. Algebra 1 81 Common Core Assessment Readiness

26 Name Date Class 6. The people at a conference use the following exercise to get to know each other. The leader of the conference chooses 4 people, greets each of them with a handshake, and they chat. After one minute, those 4 people each choose 4 people, greet each with a handshake, and chat. This continues until each person at the conference has shaken someone s hand. Write an exponential function that models the number of handshakes H in the nth minute. 7. A population of 300 sea turtles grows by 5% each year. a. Describe the steps needed to calculate the population each year. b. Write a recursive function for the population P after t years. 8. Simon wants to use 500 feet of fencing to enclose a rectangular area in his backyard. a. Write a function for the enclosed area A, in square feet, in terms of the width w, in feet. Show your work. b. What are the dimensions of the largest rectangle Simon can enclose with 500 feet of fencing? Explain. Algebra 1 82 Common Core Assessment Readiness

27 Name Date Class F.BF.1b* SELECTED RESPONSE Select the correct answer. 1. A rectangle has side lengths (x + 4) feet and (2x + 1) feet for x > 0. Write a function that describes the area A, in square feet, in terms of x. A(x) = 3x + 5 A(x) = 6x + 10 A(x) = 2x 2 + 9x + 4 A(x) = 2x 2 + 7x 4 2. In a factory, the cost of producing n items is C(n) = 25n Which function describes the average cost of producing one item when n items are produced? An ( )= 25n +150 A(n) = n An ( )= 25n n A(n) = 25 n n 2 Select all correct answers. 3. Two identical water tanks each hold 10,000 liters. Tank A starts full, but water is leaking out at a rate of 10 liters per minute. Tank B starts empty and is filled at a rate of 13 liters per minute. Which functions correctly describe the combined volume V of both tanks after t minutes? V(t) = 10,000 10t + 13t V(t) = 10,000 10t 13t V(t) = 10, t 13t V(t) = 10,000 3t V(t) = 10, t V(t) = 10,000 23t Select the correct answer for each lettered part. 4. Let f(x) = x 2 x 2 and g(x) = x 2 + x 6. Classify each function below as linear, quadratic, or neither. a. f(x) + g(x) Linear Quadratic Neither b. f(x) g(x) Linear Quadratic Neither c. f (x) g(x) Linear Quadratic Neither d. f(x) i g(x) Linear Quadratic Neither CONSTRUCTED RESPONSE 5. Let f(x) = x 2 + x 6 and g(x) = x 2 4. Find f(x) + g(x) and f(x) g(x). Simplify your answers. Algebra 1 83 Common Core Assessment Readiness

28 Name Date Class 6. Esther exercises for 45 minutes. She rides her bike at 880 feet per minute for t minutes and then jogs at 400 feet per minute for the rest of the time. a. Write a function that describes the distance d 1, in feet, that Esther travels while riding her bike for t minutes. b. Write a function that describes the distance d 2, in feet, that Esther travels while jogging. c. Use your answers from parts a and b to write a function that describes the distance d, in feet, that Esther travels while exercising. 7. Trina deposits $1500 in an account that earns 5% interest compounded annually. Pablo deposits $1800 in an account that earns 2.5% interest compounded annually. Write a function that models the difference D, in dollars, between the balance of Trina s account and the balance of Pablo s account after t years. (Hint: The difference between the two balances should always be positive.) 8. Town A and town B both had a population of 15,000 people in the year The population of town A increased by 2.5% each year. The population of town B decreased by 3.5% each year. a. Write a function A(t), the population of town A t years after b. Write a function for B(t), the population of town B t years after c. Find A(t) + B(t) and A(t) B(t). Simplify your answers and interpret each function in terms of the situation. If necessary, round decimals to the nearest thousandth. Algebra 1 84 Common Core Assessment Readiness

29 Name Date Class F.BF.2* SELECTED RESPONSE Select the correct answer. 1. A theater has 18 rows of seats. There are 22 seats in the first row, 26 seats in the second row, 30 seats in the third row, and so on. Which of the following is a recursive formula for the arithmetic sequence that represents this situation? f(0) = 18, f(n) = f(n 1) + 4 for 1 n 18 f(1) = 22, f(n) = f(n 1) + 4 for 2 n 18 f(n) = n f(n) = (n 1) 2. The table below shows the balance b, in dollars, of Daryl s savings account t years after he made an initial deposit. What is an explicit formula for the geometric sequence that represents this situation? Time, t (years) Balance, b (dollars) 1 $ $ $ $ b(t) = 1.015(1218) t 1 b(t) = 1218(1.015) t b(t) = (t 1) b(t) = 1218(1.015) t 1 Select all correct answers. 3. Amelia earns $36,000 in the first year from her new job and earns a 6% raise each year. Which of the following models Amelia s pay p, in dollars, in year t of her job? p(0) = 36,000, p(t) = 1.06 i p(t 1) for t 1 p(1) = 36,000, p(t) = 1.06 i p(t 1) for t 2 p(t) = 36,000 i 1.06 t 1 for t 1 p(t) = 1.06 i 36,000 t 1 for t 1 p(t) = 1.06(t 1) + 36,000 for t 1 p(t) = 38,160 i 1.06 t 2 for t 1 CONSTRUCTED RESPONSE 4. Calvin is practicing the trumpet for an audition to play in a band. He starts practicing the trumpet 40 minutes the first day and then increases his practice time by 5 minutes per day. The audition is on the 10th day. a. Write a recursive rule that represents the time t, in minutes, Calvin practices on day d. b. Write an explicit rule that represents the time t, in minutes, Calvin practices on day d. c. Use the result from part b to find how long Calvin practices on the 8th day. Show your work. Algebra 1 85 Common Core Assessment Readiness

30 Name Date Class 5. The table displays the speed of a car s, in feet per second, t seconds after it starts coasting. Time, t (seconds) Speed, s (ft/sec) a. Explain why this sequence is geometric. b. Write an explicit rule for this sequence using the values from the table. c. Use the result from part b to write a recursive rule for this sequence. d. What is the speed of the car when it begins to coast? Show your work. 6. The table below shows the cost c, in dollars, of a private party on a boat based on the number of people p attending. People, p Cost, c (dollars) a. Does an arithmetic sequence or a geometric sequence model this situation? Justify your answer by using the values in the table. b. Write an explicit formula and a recursive formula for the sequence. Show your work. c. How much would it cost for 44 people to attend the private party? Show your work. Algebra 1 86 Common Core Assessment Readiness

31 Name Date Class F.BF.3 SELECTED RESPONSE Select the correct answer. 1. The graph of g(x) is shown below. The graph of g(x) can be obtained by applying horizontal and vertical shifts to the parent 3 function f (x) = x. What is g(x)? CONSTRUCTED RESPONSE 3. Describe the transformations applied to the graph of the parent function f (x) = x used to graph g(x) = 2 1 x + 3. Graph g(x). 3 g(x) = x 2 3 g(x) = x g(x) = x g(x) = x What must be done to the graph of f(x) = x to obtain the graph of the function g(x) = 0.5 x ? The graph of f(x) is shifted left 4 units, horizontally shrunk by a factor of 0.5, and shifted down 10 units. The graph of f(x) is shifted right 4 units, vertically shrunk by a factor of 0.5, and shifted down 10 units. The graph of f(x) is shifted left 4 units, vertically shrunk by a factor of 0.5, and shifted down 10 units. The graph of f(x) is shifted left 4 units, vertically shrunk by a factor of 0.5, and shifted up 10 units. 4. Describe how the nonzero slope m of a linear function g(x) = mx is a transformation of the graph of the parent linear function f(x) = x. Algebra 1 87 Common Core Assessment Readiness

32 Name Date Class 5. For the following graphs of transformed functions, state the parent function f(x), the type of transformation, and write a function rule. a. 6. a. Rewrite g(x) = 1 2 x2 2x + 2 in vertex form. Show your work. b. b. Describe the transformations applied to the parent function f(x) = x 2. c. Graph g(x). Algebra 1 88 Common Core Assessment Readiness

33 Name Date Class F.BF.4a SELECTED RESPONSE Select the correct answer. 1. What is the inverse of f(x) = 2x + 6? g(x) = 1 2 x 3 g(x) = 1 2 x + 3 g(x) = 2x 6 g(x) = 1 2 x The point (2, 12) is on the graph of f(x). Which of the following points must be on the graph of g(x), the inverse of f(x)? ( 2, 12) (2, 12) (2, 12) (12, 2) Select all correct answers. 3. If f (x) = 1 x + 5, which of the following 8 statements about g(x), the inverse of f(x), are true? g( 2.125) = 57 g( 0.5) = 44 g( 0.375) = 37 g(0.125) = 39 g(0.625) = 45 g(1.125) = 40 CONSTRUCTED RESPONSE 4. Let f(x) = 13x Find the inverse of f(x) and use it to find a value of x such that f(x) = 182. Show your work. 5. At a carnival, you pay $15 for admission, plus $3 for each ride you go on. a. Write a function A(r) that models the amount A, in dollars, you would spend to ride r rides at the carnival. b. Find the inverse of A(r). Show your work. c. What does the inverse function found in part b represent in the context of the problem? Algebra 1 89 Common Core Assessment Readiness

34 Name Date Class 6. The graph of f(x) = 3x 6 is shown, along with the dashed line y = x. 7. a. Find g(x), the inverse of f(x) = mx + b. Show your work. a. Find g(x), the inverse of f(x). Show your work. b. Graph g(x) on the coordinate grid above. c. How are the graphs of f(x) and g(x) related to the line y = x? b. Use the formula for g(x) to find the inverse of f(x) = 4x c. Does every linear function have an inverse? Use your result from part a to explain why or why not. If not, give the general forms of any linear functions that do not. Algebra 1 90 Common Core Assessment Readiness

35 Name Date Class F.LE.1a* SELECTED RESPONSE Select the correct answer. 1. For some exponential function f(x), f(0) = 12, f(1) = 18, and f(2) = 27. How does f(x) change when x increases by 1? f(x) grows by a factor of 2 3. f(x) grows by a factor of 3 2. f(x) increases by 6. f(x) increases by The balance B of an account earning simple interest is $1000 when the account is opened, $1075 after one year, and $1150 after two years. How does the balance of the account change from one year to the next? The balance increases by 7.5%. The balance decreases by 7.5%. The balance increases by $75. The balance increases by $150. Select all correct answers. 3. Marco starts reading a 350-page book at 9 a.m. The number of pages P Marco has left to read t hours after 9 a.m. is modeled by the function P(t) = t. During which of the following time periods does Marco read the same number of pages he reads between 11 a.m. and 1 p.m.? 9 a.m. to 11 a.m. 11 a.m. to 12 noon 12:30 p.m. to 1:30 p.m. 2 p.m. to 4 p.m. 1:30 p.m. to 3.30 p.m. Match each statement in the proof with the correct reason below. Given: x 2 x 1 = x 4 x 3, f(x) = ab x Prove: f (x ) 2 f (x 1 ) = f (x ) 4 f (x 3 ) 4. x 2 x 1 = x 4 x 3, f(x) = ab x 5. b x 2 x 1 = bx 4 x 3 6. bx 2 b x 1 7. abx 2 ab x 1 = bx 4 b x 3 = abx 4 ab x 3 8. f (x 2 ) f (x 1 ) = f (x 4 ) f (x 3 ) A Given B Power of powers property C Distributive property D Subtraction property of equality E Definition of f(x) F Quotient of powers property G If x = y, then b x = b y H Multiplication property of equality Algebra 1 91 Common Core Assessment Readiness

36 Name Date Class CONSTRUCTED RESPONSE 9. Complete the reasoning to prove that linear functions grow by equal differences over equal intervals. Given: x 2 x 1 = x 4 x 3 f(x) is a linear function of the form f(x) = mx + b. Prove: f(x 2 ) f(x 1 ) = f(x 4 ) f(x 3 ) x 2 x 1 = x 4 x 3 Given m(x 2 x 1 ) = m(x 4 x 3 ) mx 2 mx 1 = mx 4 mx 3 mx 2 + b mx 1 b = mx 4 + mx 3 Addition and subtraction properties (mx 2 + b) (mx 1 + b) = Distributive property f (x 2 ) f (x 1 ) = Definition of f (x) 10. Sandra s annual salary S, in dollars, after working at the same company for t years is given by the function S(t) = 38, t. a. Complete the table showing Sandra s salary after each year for the first five years. Time, t (years) Salary, S (dollars) b. Show that Sandra s salary increases by the same amount each year. 11. The population of a certain town is 3500 people in The population of the town P is modeled by the function P(t) = 3500(0.97) t, where t is the number of years after a. By what factor did the population change between 2000 and 2001? Between 2001 and 2002? Round your answers to the nearest hundredth. Show your work. What do you notice? b. By what factor did the population change between 2000 and 2002? Between 2001 and 2003? Round your answers to the nearest hundredth. Show your work. What do you notice? Algebra 1 92 Common Core Assessment Readiness

37 Name Date Class F.LE.1b* SELECTED RESPONSE Select the correct answer. 1. In which of the following situations does Michael s salary change at a constant rate relative to the year? Michael s starting salary is $9500 and increases by 4% each year. Michael s starting salary is $9500 and increases by $500 each year. Michael s starting salary is $9500. He receives a $500 raise after one year and a $600 raise after the second year. Michael s starting salary is $9500. He receives a 4% raise after one year and a 5% raise after the second year. 2. The table shows the population of two cities. Which city s population is changing at a constant rate per year? Year City A City B , , , , , , , ,000 A B Both A and B Neither A nor B Select all correct answers. 3. Determine which situations describe an amount of money changing at a constant rate relative to a unit change in time of the specified unit. The value of David s car decreases by 11% each year. Susan adds $50 to a savings account each week. The price of a stock each week is 105% of its price from the previous week. Monica pays $700 for car insurance the first year and pays an additional $10 per year. The amount Ariel and Miguel pay to rent a car for $40 a day. CONSTRUCTED RESPONSE 4. For which of these functions does the function value change at a constant rate per unit change in x? Explain. x f(x) g(x) h(x) Algebra 1 93 Common Core Assessment Readiness

38 Name Date Class 5. Samantha started a new job, and is paid $10.50 an hour. Each month, Samantha earns a $0.25 per hour raise. Does Samantha s hourly pay grow at a constant rate per unit change in month? Explain. 6. Alonzo and Katy hike 4 miles in 2 hours and then break to eat lunch. After lunch, they hike for 45 minutes and travel 1.5 miles. Not including the time spent eating lunch, do Alonzo and Katy hike at a constant rate? If not, explain why not. If so, what is the unit rate? 7. Tim works as a salesperson for a furniture store. His first year, he earns a base pay of $25,000 plus a 5% commission on every item he sells. His second year, he earns a base pay of $26,000 plus a 6.5% commission. His third year, he earns a base pay of $27,040 plus an 8% commission. Decide if each of the quantities below changes at a constant rate per unit change in year. Explain your answers. a. Tim s base pay. 8. Companies A and B each employ 500 workers. Company A decides to increase its workforce by 10% each year. Company B decides to increase its workforce by 50 workers each year. a. Complete the table to show each company s workforce for the first 3 years after implementing the plan to increase its workforce. Round down to the nearest person. Year Company A Company B b. For each company, find the amount by which the workforce changed each year. Which company s workforce has a constant rate of growth per unit change of year? Show your work. b. Tim s commission rate. c. Use your results from part b to determine that company s workforce 4 years after implementing the plan to increase its workforce. Algebra 1 94 Common Core Assessment Readiness

39 Name Date Class F.LE.1c* SELECTED RESPONSE Select the correct answer. 1. In which of the following situations does Pam s hourly wage change by a constant percent per unit change in year? Pam s starting hourly wage is $14.50 per hour the first year, and it increases by $1.50 each year. Pam s starting hourly wage is $ She receives a $0.50 per hour raise after one year, a $0.75 per hour raise after the second year, a $1.00 per hour raise after the third year, and so on. Pam s hourly wage is $20 per hour in the first year, $22 per hour the second year, $24.20 per hour the third year, and so on. Pam s starting hourly wage is $ Her hourly wage is $15.75 after one year, $17.00 after two years, $18.75 after three years, and so on. 2. The table shows the value, in dollars, of three cars after they are purchased. Which car s value decreases by a constant percent? Year Car A Car B Car C 0 $21,000 $18,000 $25,000 1 $18,000 $15,625 $22,500 2 $15,000 $13,250 $20,250 Car A Car B Car C Cars B and C Select all correct answers. 3. Which of the following situations describe a quantity that increases by a constant percent that is at least 20% per unit time? There are 400 bacteria in a Petri dish the first day, 700 the second day, 1225 the third day, and so forth. The number of fish in the lake is 24 the first year, 48 in the second year, 72 in the third year, and so on. The number of visitors for a website is 4000 one month, 5200 the second month, 6760 the third month, and so on. The price for a gallon of cooking oil is $3.00 the first year, $3.30 the second year, $3.63 the third year, and so on. The population of a town is 10,000 the first year, 11,500 the second year, 13,225 the third year, and so on. CONSTRUCTED RESPONSE 4. For which of these functions does the function value change at a constant factor per unit change in x? Explain. x f(x) g(x) h(x) Algebra 1 95 Common Core Assessment Readiness

40 Name Date Class 5. In one year, a population of endangered turtles laid 8000 nests. Each year, the number of nests is half as many as the number of nests in the previous year. Does the number of nests change by a constant percent per unit change in a year? Explain. 6. The table shows the mass, in grams, of the radioactive isotope carbon-11 after it starts decaying. Does the mass of the substance decay by a constant percent each minute? If so, find the decay rate. Explain and round to the nearest hundredth of a percent. If not, explain why not. Time (minutes) Mass (grams) Carol inherited three antiques one year. The value, in dollars, of each antique for the first few years after she inherited the antiques is shown in the table. Time (years) Antique toy Antique vase Antique chair 0 $70.00 $25.00 $ $77.00 $30.00 $ $84.70 $37.50 $ $93.17 $47.50 $ Which antiques have a value that grows by a constant factor relative to time? Of those antiques, which antique increases its value at a faster rate? Explain your answers. 8. Two competing companies redesigned their websites during the same month. The table shows the number of visits each website receives per month after the redesigns. Jeff thinks that the number of visits for both websites grows by a constant percent per month. Month Company A Company B 0 120, , , , , , , ,166 a. Is Jeff correct about company A? Justify your answer. b. Is Jeff correct about company B? Justify your answer. Algebra 1 96 Common Core Assessment Readiness

41 Name Date Class F.LE.2* SELECTED RESPONSE Select all correct answers. 1. Emile is saving money to buy a bicycle. The amount he has saved is shown in the table. Which of the functions below describe the amount A, in dollars, Emile has saved after t weeks? Weeks Amount 1 $30 2 $45 3 $60 4 $75 5 $90 6 $105 A(t) = (t 1) A(t) = (t 1) A(t) = t A(t) = t A(t) = 30(1.5) t A(t) = 15(2) t Select the correct answer. 2. Which function models the relationship between x and f(x) shown in the table? x f(x) f (x) = 1 x f(x) = 2x 3 2 f(x) = x 1 f(x) = 4x 7 3. Sasha invests $1000 that earns 8% interest compounded annually. Which function describes the value V of the investment after t years? V(t) = t V(t) = 1000(0.08) t V(t) = 1000(0.92) t V(t) = 1000(1.08) t CONSTRUCTED RESPONSE 4. A $100 amount is invested in two accounts. Account 1 earns 0.25% interest compounded monthly, and account 2 earns 0.25% simple interest monthly. Write two functions that model the balances B 1 and B 2 of both accounts, in dollars, after t months. 5. An initial population of 1000 bacteria increases by 25% each day. a. Is the population growth best modeled by a linear function or an exponential function? Explain. b. Write a function that models the population P after t days. 6. The value of a stock over time is shown in the table. Write an exponential function that models the value V, in dollars, after t years. Show your work. Time, in years Value, in dollars Algebra 1 97 Common Core Assessment Readiness

42 Name Date Class 7. The number of seats in each row of an auditorium can be modeled by an arithmetic sequence. The 5th row in this auditorium has 36 seats. The 12th row in this auditorium has 64 seats. Write an explicit rule for an arithmetic sequence that models the number of seats s in the nth row of the auditorium. Show your work. 9. The neck of a guitar is divided by frets in such a way that pressing down on each fret changes the note produced when the guitar is played. The first fret of a guitar is placed mm from the end of the guitar s neck. The second fret is placed mm from the first fret. The distances, d, in millimeters, of the first four frets relative to the previous fret are shown in the graph below. 8. The art club is creating and selling a comic book as part of a fundraiser. The graph shows the profit P earned from selling c comic books. a. Use the graph to write a linear function P(c) that models the profit P from selling c comic books. b. What is the real-world meaning of the slope and P-intercept of your function? c. How many comic books does the club have to sell in order to make $375? Show your work. a. Consider the sequence of distances between the frets. Is the sequence arithmetic or geometric? Find a common difference or ratio to justify your answer. b. Write an explicit rule for d(n), the distance between fret n and the fret below it. Show your work. c. Use your rule from part b to determine the distance between the 19th and 20th frets. Algebra 1 98 Common Core Assessment Readiness

43 Name Date Class F.LE.3* SELECTED RESPONSE Select all correct answers. 1. The value V A of stock A t months after it is purchased is modeled by the function V A (t) = t The value V B of stock B t months after it is purchased is modeled by the function V B (t) = 10(1.25) t. Based on the model, for which t-values is the value of stock B greater than the value of stock A? t = 5 t = 6 t = 7 t = 11 t = 12 Select the correct answer. 2. f(x) = 2x and g(x) = 2 x are graphed on the grid below. For what x-values is g(x) > f(x)? 3. As x increases without bound, which of the following eventually has greater function values than all the others for the same values of x? f(x) = 3x 2 f(x) = 2x 3 f(x) = 3(2 x ) f(x) = 3x + 2 Select the correct answer for each lettered part. 4. Two websites launched at the beginning of the year. The number of visits A(t) to website A is given by some exponential function, where t is the time in months after the website is launched. The number of visits B(t) to website B is given by some quadratic function. The graph of each function is shown below. For each of the given t-values, compare A(t) and B(t). x > 4 x > 2 0 < x < 2 and x > 4 2 < x < 4 a. t = 2 A(t) < B(t) A(t) > B(t) b. t = 3 A(t) < B(t) A(t) > B(t) c. t = 4 A(t) < B(t) A(t) > B(t) d. t = 5 A(t) < B(t) A(t) > B(t) e. t > 12 A(t) < B(t) A(t) > B(t) Algebra 1 99 Common Core Assessment Readiness

44 Name Date Class CONSTRUCTED RESPONSE 5. The population A of town A and the population B of town B t years after 2000 is described in the table. Time, t (years) Town A population, A(t) Town B population, B(t) a. Write functions for A(t) and B(t). 6. Let f(x) = x + 4, g(x) = x 4, and h(x) = 4 x for x 0. a. Graph f(x) and h(x). b. Graph g(x) and h(x). b. Use your functions from part a to complete the table, rounding to the nearest person. c. If the populations continue to increase in the same way, how do the populations compare for every year after 2008? Explain how you can tell without calculating the populations for every year. c. How do the values of h(x) compare to the values of f(x) and g(x) as x increases without bound? d. Use the graphs and your answer from part c to make a conjecture about how the values of exponential functions compare to the values of linear and polynomial functions as x increases without bound. Algebra Common Core Assessment Readiness

45 Name Date Class F.LE.5* SELECTED RESPONSE Select the correct answer. 1. The function A(d) = 0.45d models the amount A, in dollars, that Terry s company pays him based on the roundtrip distance d, in miles, that Terry travels to a job site. How much does Terry s pay increase for every mile of travel? $0.45 $ $ $ Drake is considering buying one of the four popular e-readers where the e-reader s premium services is a monthly charge. The functions A 1 (t) = 5t + 350, A 2 (t) = 10t + 250, A 3 (t) = 499, and A 4 (t) = 15t model the total amount of money A, in dollars, that Drake spends after buying the e-reader and subscribing to t months of the e-reader s premium services. Which e-reader has the greatest monthly subscription cost? E-reader 1 with cost A 1 (t) E-reader 2 with cost A 2 (t) E-reader 3 with cost A 3 (t) E-reader 4 with cost A 4 (t) 3. Each bacterium in a petri dish splits into 2 bacteria after one day. The function b(d) = 600 i 2 d models the number of bacteria b in the petri dish after d days. What is the initial number of bacteria in the petri dish? Select all correct answers. 4. The function a(t) = 44,000(1.045) t models Johanna s annual earnings a, in dollars, t years after she starts her job. Which of the following statements are true about Johanna s salary? Johanna initially earns $44,000 per year. Johanna initially earns $45,980 per year. Johanna s salary increases by 1.045% per year. Johanna s salary increases by 4.5% per year. Johanna s salary increases by 104.5% per year. CONSTRUCTED RESPONSE 5. The function h(t) = 1200t + 15,000 models the height h, in feet, of an airplane t minutes after it starts descending in order for it to land. What is the height of the airplane when it begins to descend? Explain. 6. The function P(r) = represents the number of players P remaining after r single-elimination rounds of a tennis tournament. a. What is the initial number of players in the tournament? Explain. b. What fraction of players remaining after r 1 rounds are eliminated in the rth round? Explain. r Algebra Common Core Assessment Readiness

46 Name Date Class 7. The function P(r) = 1250(0.98) t models the premium P, in dollars, that Steven pays for automotive insurance each year after having the insurance for t years. a. What is the amount that Steven pays for the first year of his insurance coverage? b. What is the percentage decrease of Steven s premium every year? Explain. 8. A family is traveling in a car at a constant average speed during a road trip. The function d(t) = 65t models the distance d, in miles, the family is from their house t hours after starting to drive on the second day of the road trip. a. At what average speed is the family s car traveling? Explain. 9. A census from the government determines the official population of jurisdictions. The census is taken once every decade. The function A(c) = 50,600(1.08) c models the official value for the population of city A, where c is the number of censuses taken since the first census. Similarly, B(c) = 75,850(1.069) c models the official value for the population of city B. a. Which city had a larger population in the first census? Explain. b. Which city s official value for its population is growing at a faster rate between the censuses? Explain. b. What is the distance between the family s house and the point where they started driving on the second day? Explain. Algebra Common Core Assessment Readiness

47 F.IF.1 Answers 1. B 2. A 3. B, D, F, G 4. A function assigns each value from the domain to exactly one value in the range. The relation is not a function because February has 28 days in a common year and 29 days in a leap year. 1 point for stating its not a function; 2 points for explanation 5. The table represents a function. The domain is { 2, 1, 0, 1, 2}. The range is {2, 6, 10, 14, 18}. 1 point for answer; 1 point for domain; 1 point for range 6. The y-value associated with x = 2 is 4. The y-value associated with x = 0 is 3. The y-value associated with x = 2 is 2. If y = f(x), then the x-values are in the domain of f(x), and the y-values are in the range of f(x). 1 points for each y-value; 1 point for stating the x-values are in the domain of f(x); 1 point for stating the y-values are in the range of f(x) 7. The domain of the function is the set of all real numbers. The range is the set of real numbers greater than 3. 1 point for the domain; 2 points for the range 8. a. This is a function because no coin has more than one monetary value. The domain is the set of coins {penny, nickel, dime, quarter, half dollar}. The range is the set of monetary values assigned to each coin, {$0.01, $0.05, $0.10, $0.25, $0.50}. (Students may or may not include half dollar and dollar coins in their example. Assign full credit as long as penny, nickel, dime, and quarter are included.) b. This is not a function because each bill is equivalent to many different combinations of coins. For example, a 1 dollar bill is equivalent to 100 pennies, but it is also equivalent to 10 dimes. a. 1 point for answer; 1 point for explanation; 1 point for the domain; 1 point for the range b. 1 point for answer; 1 point for explanation Algebra 1 Teacher Guide 39 Common Core Assessment Readiness

48 Name Date Class F.IF.2 Answers 1. A 2. C 3. C 4. B, D, F, H 5. C(15) = 25(15) = 375 This value represents the production cost of 15 graphing calculators. So, it costs $375 to produce 15 graphing calculators. 1 point for value; 1 point for interpretation 6. f( 2) = 13( 2) ( 2) 2 = 26 4 = 30 f( 1) = 13( 1) ( 1) 2 = 13 1 = 14 f(0) = 13(0) 0 2 = 0 0 = 0 f(1) = 13(1) 1 2 = 13 1 = 12 f(2) = 13(2) 2 2 = 26 4 = 22 The range of the function is { 30, 14, 0, 12, 22}. 0.5 point for each value in the range; 0.5 point for work 7. a. The domain of the function is {2, 3, 4, 5, 6, 7}. b. V(2) = 2 3 = 8 cubic feet V(3) = 3 3 = 27 cubic feet V(4) = 4 3 = 64 cubic feet V(5) = 5 3 = 125 cubic feet V(6) = 6 3 = 216 cubic feet V(7) = 7 3 = 343 cubic feet a. 1 point b. 0.5 point for each value 8. a. The profit function is: P(n) = n 25(99.50) = n b. The domain of the function is all whole numbers between 0 and 25, inclusive. The store cannot sell a negative number of televisions and they can only sell up to the number in stock, which is 25. c. The store will make a profit of $1, a. 1 point b. 1 point for domain; 1 point for explanation c. 1 point 9. a. Set p(t) equal to zero and solve for t. 0 = 8t = 8t t = 12.5 It would take 12.5 minutes for the printer to use all 100 sheets. b. The domain of the function is all values of t, where 0 t The printer takes 12.5 minutes to print all 100 pages, so the upper bound on t is The printer starts printing at 0 minutes, so the lower bound is 0. c. The range of the function is all values of p(t), where 0 p(t) 100. There are 100 sheets of paper in the printer at the start, so the upper bound on p(t) is 100. There cannot be a negative number of sheets, so the lower bound on p(t) is 0. d. The printer will have p(7) = 8(7) = = 44 sheets of paper left. So, Tanya s report is = 56 pages long. a. 1 point for answer; 1 point for explanation b. 1 point for domain; 1 point for explanation c. 1 point for range; 1 point for explanation d. 1 point for answer; 1 point for work Algebra 1 Teacher Guide 40 Common Core Assessment Readiness

49 F.IF.3 Answers 1. B 2. D 3. A, C 4. B 5. D 6. F 7. A 8. E 9. a. f(n) = n b. f(14) = = 197 a. 1 point b. 1 point 10. a Since the domain starts with 1, f(3) is the third term of the sequence, which is 4 5. b. When the domain starts with 0, f(3) is the fourth term of the sequence, 5 6. a. 1 point for answer; 1 point for explanation b. 1 point 11. a. Each term in the Fibonacci sequence is the sum of the previous two terms, and the first two terms are 1. A recursive function that describes this is f(0) = f(1) = 1, f(n) = f(n 1) + f(n 2), n 2. b. 2, 2, 4, 6, 10 c. Each term in the new sequence is still the sum of the previous two terms (4 = 2 + 2, 6 = 4 + 2, 10 = 6 + 4, and so on), so the function from part b can be described as f(0) = f(1) = 2, f(n) = f(n 1) + f(n 2), n 2. a. 1 point b. 1 point c. 2 points for explanation 12. a. f(n) = 2n 1 b. f(1) = 1, f(n) = f(n 1) + 2 for n 2 and n is an integer. a. 2 points b. 2 points Algebra 1 Teacher Guide 41 Common Core Assessment Readiness

50 F.IF.4* Answers 1. C 2. A, C, G a. The C(t)-intercept is $15, which is the cost for sending up to 1000 texts. 2 points for graph; 1 point for intercept; 1 point for interpretation 4. The profit increases as the orchard goes from 0 to 40 trees. Then, the profit decreases from 40 to 80 trees. The owner of the orchard earned the least profit when there were no trees planted and when there were 80 trees planted. The most profit was earned when there were 40 trees planted. 2 points for description of relationship; 2 points for stating where the orchard owner earned the least profit; 1 point for stating where the orchard owner earned the most profit b. The function is decreasing for x < 0 and increasing for 0 < x. c. f(x) is positive for all values of x except 0. d. f(x) will never be negative because absolute value can never be negative. a. 1 point b. 1 point for stating where f(x) decreases; 1 point for stating where f(x) increases c. 1 point d. 2 points Algebra 1 Teacher Guide 42 Common Core Assessment Readiness

51 F.IF.5* Answers 1. C 2. D 3. C 4. a. The domain is t such that 0 t 7. b. The domain represents the time that the object is in the air. 1 point for each part 5. The domain is the real numbers. The range is the real numbers greater than 2. 1 point for the domain; 1 point for the range 6. a. P(c) = 350c 1800 b. The domain of P(c) is the whole numbers. The company cannot sell a negative number of the tablet computers and they cannot sell a fractional number of tablet computers. c. 1800, 1450, 1100, 750, 400, 50, 300, 650 a. 2 points for the function b. 1 point for the domain; 1 point for the explanation; c. 2 points for range values 7. Brand A A(h) = 4.19h The domain of A(h) is the nonnegative real numbers since brand A can be purchased in any nonnegative amount from the deli counter. Brand B B(h) = 4.79h The domain of B(h) is {0, 0.5, 1, 1.5, } since brand B can only be purchased in increments of either 0.5 pound or 1 pound. 1 point for each function rule; 1 point for each domain; 1 point for each explanation Algebra 1 Teacher Guide 43 Common Core Assessment Readiness

52 F.IF.6* Answers 1. B 2. A 3. C 4. C, D, E 5. a. No b. Yes c. No d. Yes e. No 6. a. Anchorage: about 5.6 minutes of daylight per day Los Angeles: about 2.0 minutes of daylight per day b. On average, Anchorage loses about 5.6 minutes of daylight each day during the month of October, while Los Angeles loses about 2 minutes of daylight each day. c. Since October 17 is 16 days after October 1, evaluate the expression ( 2.0)(16) to get 679 minutes, or 11 hours 19 minutes, of daylight on October 17. If the sun rises at 7:00 A.M. that day, then it sets about 11 hours and 19 minutes later, or at 6:19 P.M. a. 0.5 point for each average rate of change; b. 1 point c. 1 point for finding the minutes of daylight; 1 point for the description of how to find the minutes of daylight; 1 point for the time of sunset 7. a. The average growth rate between weeks 2 and 3 is about = = bacteria per week. b. The average growth rate between weeks 3 and 4 is about = = bacteria per week. c. The average growth rate between weeks 4 and 5 is about = = bacteria per week. d. The average growth rate is doubling as each week passes. 2(2000) = 4000 bacteria per week, 2(4000) = 8000 bacteria per week e. The average growth rate between weeks 5 and 6 will probably be 16,000 bacteria per week if the pattern continues. a. 0.5 point b. 0.5 point c. 0.5 point d. 1 point for answer; 2 points for justification e. 0.5 point Algebra 1 Teacher Guide 44 Common Core Assessment Readiness

53 F.IF.7a* Answers 1. B 2. A 3. a. R(n) = 5.25n b. Since Sally is selling 1 necklace at a time and cannot sell negative necklaces, a reasonable domain for this function is the whole numbers. c. R(n) d n 25 d. The n- and R-intercepts are both 0. The intercept indicates that Sally will earn no revenue if she sells no necklaces. a. 1 point b. 1 point c. 1 point d. 1 point for the intercept; 1 point for the explanation 4. a. The t-intercepts are 0 and 5. These intercepts indicate that the object has a height of 0 meters when the object is thrown (t = 0) and again at 5 seconds after it is thrown. The h-intercept is the same as the first t-intercept. b. The vertex is (2.5, ). c. The vertex is a maximum. This means that the maximum height of the object is feet. a. 1 point for each t-intercept; 0.5 point for each interpretation b. 1 point for the vertex c. 0.5 point for the answer; 0.5 point for the interpretation d. 2 points for correct graph 5. One side of the rectangular enclosure is s. Let the other side of the enclosure be x. The perimeter of the combined enclosures is 1200 = 5s + 2x. Solve for x: 1200 = 5s + 2x s = 2x 0.5(1200 5s) = x s = x The width of the rectangular enclosure is s + x = s s = s. The combined area of the enclosures is A(s) = s( s) = 600s 1.5s 2 = 1.5s s Algebra 1 Teacher Guide 45 Common Core Assessment Readiness

54 The square enclosure will be 200 feet by 200 feet. The rectangular enclosure will be 100 feet by 200 feet. The vertex of the function, (200, 60000), is a maximum. This means that the combined area of the enclosures is maximized when s = 200. Since s is the side length of the square, the square is 200 feet by 200 feet. Since the rectangle shares a side with the square, one of its dimensions is 200 feet. The other is given by the expression s (200) = = 100 Thus, the rectangle is 100 feet by 200 feet. 2 points for the function; 1 point for the graph; 1 point for each set of dimensions; 2 points for explanation involving the vertex Algebra 1 Teacher Guide 46 Common Core Assessment Readiness

55 F.IF.7b* Answers 1. B 2. D 3. B Possible answer: 1 x < x < 1 f (x) = 1 1 x < 2 2 x 2 The domain is the real numbers and the range is { 2, 1, 4}. 1 point for graph; 1 point each for the domain and range 5. 3 points for the function; 1 point for the graph 7. The reaction time increases as the distance increases. The graph of t(d) is increasing for d > 0. 1 point for graph; 1 point for answer; 1 point for explanation involving graph The function is increasing on its entire domain. Thus, the function is never decreasing. 1 point for the graph; 2 points for recognizing the graph is always increasing Algebra 1 Teacher Guide 47 Common Core Assessment Readiness

56 F.IF.7e* Answers 1. C 2. B 3. A, C, E 4. Possible answer: An exponential function has either one x-intercept or no x-intercepts. The functions f(x) = 2 x + 2 and g(x) = 2 x 2 illustrate this in the following graph. f(x) = 2 x + 2 has no x-intercepts, while g(x) = 2 x 2 has one x-intercept. 5. a. b. The V(t)-intercept is This is the value of the copier at the time of purchase, $1200. a. 2 points for the graph b. 1 point for the V(t)-intercept; 1 point for the interpretation 1 point for stating such a function can have no x-intercepts; 1 point for stating such a function can have 1 x-intercept; 1 point each for example graphs illustrating both possibilities (no symbolic definition of example functions necessary) Algebra 1 Teacher Guide 48 Common Core Assessment Readiness

57 F.IF.8a Answers 1. B 2. B 3. B, C, E 4. a. False b. True c. False d. True e. True 5. a. f (x) = 4x 2 + 4x 15 = 4x 2 +10x 6x 15 = 2x(2x + 5) 3(2x + 5) = (2x 3)(2x + 5) The zeros of the function are x = 3 2 and x = 5 2. b. The vertex is halfway between the zeros of the function, so the x-coordinate is 1. The value of the 2 function at x = 1 2 is = 16. The vertex of f(x) is 1 2, 16. The coefficient of x 2 is positive, so the parabola opens up, and the vertex is the minimum value. a. 1 point for factoring; 0.5 point for each zero b. 1 point for coordinates of the vertex; 1 point for stating that the vertex is a minimum; 1 point for explanation 6. a. Miguel is correct in saying that the function has no x-intercepts. However, the axis of symmetry can still be found by completing the square and finding the vertex. The axis of symmetry passes through the vertex. b. Complete the square: f (x) = 2x 2 16x 34 = x 2 + 8x) 34 = x 2 + 8x ) 34 = 2( x 2 + 8x +16) = 2 x + 4 ( ) 2 2 The vertex of the function is ( 4, 2), so the axis of symmetry is x = 4. a. 1 point b. 1 point for work; 1 point for answer 7. a. h(x) = x = 9 ( 125 x2 625) = 9 (x 25)(x + 25) 125 The zeros of the function occur where the sides of the arch are at the water level. They are 25 feet to the left and right of the center of the bridge, so the bridge is 50 feet long. b. The coefficient of x 2 is negative, so the vertex is a maximum value of the function. The vertex is halfway between the zeros of the function, at x = 0. h(0) = (0) = 45 feet, so the sailboat will not be able to pass under the bridge. a. 1 point for answer; 1 point for explanation involving the zeros b. 1 point for answer; 1 point for explanation involving the vertex as a maximum Algebra 1 Teacher Guide 49 Common Core Assessment Readiness

58 F.IF.8b Answers 1. A 2. B 3. A, C, E, F, H 4. a. Not equivalent b. Equivalent c. Equivalent d. Not equivalent e. Equivalent f. Not equivalent 5. a. P(t) = 3.98(1.02) t = 3.98( ) t b. The value of r is This means that the population increases by 2% annually. a. 1 point b. 1 point for answer; 1 point for interpretation ( ) ( ) 6. g(x) = x 1 = x 4 1 = 200 4x 4 = 1 200( 4x ) 4 ( ) = 1 ( 4 f (x) ) The function values of g(x) are 1 of the 4 corresponding values of f(x). 2 points for work transforming g(x); 1 point for answer 7. a. V(t) = 1500(1.035) t = 1500( ) t The annual interest rate is 3.5%. b. V(t) = 1500(1.035) t = 1500( ) t 5 t 1500(1.19) 5 The interest rate over 5 years is about 19%. a. 1 point b. 1 point for answer; 1 point for appropriate work 8. a. B(t) = 850( 1.04) t = 850( ) t The annual interest rate is 4%. ( ) t b. B(t) = = t 850(1.0033) 12t The monthly interest rate is approximately 0.33%. c. Rebecca s account will have a larger balance after 6 months. Since 0.35 > 0.33, Rebecca s account earns a greater amount of interest each month. a. 1 point for rewriting the function; 1 point for answer b. 1 point for rewriting the function; 1 point for answer c. 1 point for answer; 1 point for explanation Algebra 1 Teacher Guide 50 Common Core Assessment Readiness

59 F.IF.9 Answers 1. C 2. D 3. B, E 4. Both f(x) and g(x) are defined on the domain from 1 to 4. However, f(x) is only defined for the whole numbers 1, 2, 3, and 4, while g(x) is defined for all real numbers between 1 and 4, inclusive. The range of f(x) is the set {4, 6, 10, 18}. The range of g(x) is g(1) g(x) g(4), or 4 g(x) 19. The initial value for both functions is f(1) = 4 = = g(1). 1 point for comparing domains; 1 point for comparing ranges; 1 point for comparing initial values 5. The maximum value of the function shown in the graph is f(6) = 4. The maximum value of the function in the table is g(0) = 5. Since the maximum known value for g(x) is greater than the maximum value of f(x), g(x) has a greater maximum value on the domain 6 x 6. 1 point for answer; 1 point for explanation 6. a. Plan A costs more for 3 months. The cost of plan A for 3 months is 70(3) = $210, and the cost of plan B for 3 months is $200. b. 5 months. The cost of plan A for 1 through 6 months is A(1) = $70, A(2) = $140, A(3) = $210, A(4) = $280, A(5) = $350, and A(6) = $420. Comparing these values to the corresponding values of B(t), the first time the difference is greater than 50 is when t = 5. a. 1 point for answer; 1 point for explanation b. 1 point for answer; 2 points for explanation comparing function values Algebra 1 Teacher Guide 51 Common Core Assessment Readiness

60 F.BF.1a* Answers 1. B 2. C 3. C 4. A, D, E 5. a. T(n) = 0.1(2) n b. A(n) = 10,000 1 n 2 a. 1 point b. 1 point 6. H(n) = 4 n 2 points 7. a. Possible answer: 1. Multiply the population from the previous year by 0.05 to find the amount the population increases. 2. Add this amount to the population from the previous year. b. P(0) = 300 and P(t + 1) = 1.05P(t) for t 0 a. 2 points b. 1 point 8. a. The perimeter of the enclosed area is 500 = 2w + 2, where is the length of the enclosed area. Solve for : 2 = 500 2w = 250 w The area in terms of w is as follows: A(w) = w = (250 w)w = 250w w 2 = w w b. The graph of the function A(w) = w w is a parabola that opens down. The maximum is the function value at the vertex. Complete the square to find the vertex: A(w) = w w A(w) = (w 2 250w) A(w) = (w 2 2(125)w ) A(w) = (w 125) A(w) = (w 125) 2 +15,625 The vertex occurs at (125, 15,625). When the width is 125 feet, the area Simon can enclose is 15,625 square feet. The length of the rectangle is 250 w = = 125 feet. a. 1 point for function; 2 points for appropriate work b. 1 point for answer; 1 point for explanation Algebra 1 Teacher Guide 52 Common Core Assessment Readiness

61 F.BF.1b* Answers 1. C 2. B 3. A, E 4. a. Quadratic b. Linear c. Neither d. Neither 5. f (x) + g(x) = (x 2 + x 6) + (x 2 4) = 2x 2 + x 10 f (x) g(x) = (x 2 + x 6) (x 2 4) = x 2 + x 6 x = x 2 1 point for each answer 6. a. d 1 (t) = 880t b. d 2 (t) = 400(45 t) = 18, t c. d(t) = d 1 (t) + d 2 (t) = 880t +18, t = 480t +18,000 a. 1 point b. 1 point c. 1 point 7. Trina s account: 1500(1.05) t Pablo s account: 1800(1.025) t D(t) = 1500(1.05) t 1800(1.025) t 8. a. A(t) = 15,000(1.025) t b. B(t) = 15,000(0.965) t c. A(t) + B(t) = 15,000(1.025) t + 15,000(0.965) t = 15,000(1.025 t t ) This function describes the combined populations of towns A and B t years after A(t) B(t) = 15,000(1.025)t 15,000(0.965) t = (1.025)t (0.965) t = t t This function describes the ratio of the population of town A to the population of town B t years after a. 1 point b. 1 point c. 1 point for each function; 1 point for each interpretation (D(t) = 1800(1.025) t 1500(1.05) t is also correct.) 3 points for writing a correct difference function Algebra 1 Teacher Guide 53 Common Core Assessment Readiness

62 F.BF.2* Answers 1. B 2. D 3. B, C, F 4. a. t(1) = 40, t(d) = t(d 1) + 5, for 2 d 10 b. t(d) = 5(d 1) + 40 c. t(8) = 5(8 1) + 40 = 5(7) + 40 = = 75 Calvin practices for 75 minutes on the 8th day. a. 1 point b. 1 point c. 0.5 point for answer; 0.5 point for showing work 5. a. This sequence is geometric because the ratios of consecutive terms are approximately equal = 0.95, , The common ratio is approximately b. s(t) = 57(0.95) t 1 c. s(1) = 57, s(t) = s(t 1) i 0.95, for t 2 d. The speed of the car is 60 feet per second when it begins to coast. Substitute 0 for t in the explicit formula, s(t) = 57(0.9) t 1. s(0) = 57(0.95) 0 1 = 57(0.95) 1 = 60 1 point for each part 6. a. An arithmetic sequence models this situation because there is a common difference between every term = = = 28 b. Since the common difference is 28, the first term of the sequence is p = 2, and c(2) = 306, an explicit formula that models this situation is c(p) = (p 2) for p 2. A recursive formula that models this situation is c(2) = 306, c(p) = c(p 1) + 28, for p 3. c. Substitute 44 for p in the explicit formula, c(p) = (p 2). c(p) = (44 2) = (42) = = 1482 It would cost $1,482 for 44 people to attend the party. a. 1 point for answer; 1 point for justification b. 1 point for explicit formula; 1 point for recursive formula; 1 point for showing work c. 0.5 point for answer; 0.5 point for showing work Algebra 1 Teacher Guide 54 Common Core Assessment Readiness

63 F.BF.3 Answers 1. B 2. C 3. Possible answer: The graph of f(x) is reflected about the y-axis, shifted left 1 unit, vertically stretched by a factor of 2, reflected about the x-axis, and shifted up 3 units to obtain g(x). b. f(x) = 2 x ; vertical shift down; h(x) = 2 x 2 a. 0.5 point for parent function; 1 point for transformation; 1 point for rule b. 0.5 point for parent function; 1 point for transformation; 1 point for rule 6. a. g(x) = 1 2 x2 2x + 2 = 1 2 (x2 + 4x) + 2 = 1 2 (x2 + 4x + 4 4) + 2 = 1 2 (x + 2) = 1 2 (x + 2) = 1 2 (x + 2) points for transformations; 1 point for graph 4. The slope m acts as a vertical stretch or shrink factor. If 0 < m < 1, then the graph of g(x) is a vertical shrink of the graph of f(x) by a factor of m. If m > 1, then the graph of g(x) is a vertical stretch of the graph of f(x) by a factor of m. The sign of the slope can also transform the graph of g(x). If m < 0, then the graph of g(x) is a reflection about the x-axis of the graph of f(x). If m > 0, no reflection occurs. 2 points for description of how m can be a shrink or a stretch (either vertical or horizontal); 1 point for description of how m can be a reflection 5. a. f(x) = x; vertical shift up; g(x) = x + 3 Alternate answer: f(x) = x; horizontal shift left; g(x) = x + 3 b. Possible answer: The graph of f(x) is shifted left 2 units, vertically shrunk by c. a factor of 1, reflected across the 2 x-axis, and shifted up 4 units. a. 1 point for answer; 1 point for reasonable work b. 2 points for transformations c. 1 point Algebra 1 Teacher Guide 55 Common Core Assessment Readiness

64 F.BF.4a Answers 1. B 2. D 3. A, B, D 4. f (x) = 13x + 52 y = 13x + 52 y 52 = 13x y = x 1 13 y + 4 = x 1 13 x + 4 = y g(x) = 1 13 x + 4 The inverse of f(x) is g(x) = 1 x + 4. To 13 find a value of x such that f(x) = 182, find g(182). g(182) = 1 13 (182) + 4 = = 10 When x = 10, f(x) = point for finding the inverse of f(x); 1 point for work; 1 point for using it to find x; 1 point for work 5. a. A(r) = 3r + 15 b. r(a) = 1 3 A 5 A = 3r +15 A 15 = 3r A 15 = r 3 r = 1 3 A 5 c. This function represents the number of rides r you could go on if you plan to spend A dollars at the carnival. a. 1 point b. 1 point for answer; 1 point for work c. 2 points 6. a. f (x) = 3x 6 y = 3x 6 y + 6 = 3x y = x 1 3 y + 2 = x 1 3 x + 2 = y b. g(x) = 1 3 x + 2 c. The graphs of f(x) and g(x) are reflections across the line y = x. a. 1 point for answer; 1 point for work b. 1 point c. 1 point Algebra 1 Teacher Guide 56 Common Core Assessment Readiness

65 7. a. f (x) = mx + b y = mx + b y b = mx y b m = x 1 m y b m = x 1 m x b m = y g(x) = 1 m x b m b. g(x) = 1 4 x 11 4 c. No; the function g(x) = 1 m x b m is not defined for linear functions with a slope of 0 because the fractions with m in the denominator are not defined for m = 0. Functions of the form f(x) = c do not have inverses. a. 1 point for answer; 1 point for work b. 1 point c. 1 point for answer; 1 point for explanation; 1 point for general form Algebra 1 Teacher Guide 57 Common Core Assessment Readiness

66 F.LE.1a* Answers 1. B 2. C 3. A, D, E 4. A 5. G 6. F 7. H 8. E a. x 2 x 1 = x 4 x 3 m(x 2 x 1 ) = m(x 4 x 3 ) mx 2 mx 1 = mx 4 mx 3 mx 2 + b mx 1 b = mx 4 + b mx 3 b (mx 2 + b) (mx 1 + b) = (mx 4 + b) (mx 3 + b) f (x 2 ) f (x 1 ) = f (x 4 ) f (x 3 ) 1 point for each correctly completed part Time, t (years) Salary, S (dollars) 1 39, , , , ,500 Given b. Sandra s salary increases by $1500 each year. S(2) S(1) = 41,000 39,500 = 1500 S(3) S(2) = 42,500 41,000 = 1500 S(4) S(3) = 44,000 42,500 = 1500 S(5) S(4) = 45,500 44,000 = 1500 a. 2 points b. 1 point for answer; 1 point for appropriate work Multiplication property of equality Distributive property Addition and subtraction properties Distributive property Definition of f (x) Algebra 1 Teacher Guide 58 Common Core Assessment Readiness

67 11. a. P(0) = 3500(0.97) 0 = 3500 people P(1) = 3500(0.97) 1 = 3395 people P(1) P(0) = = 0.97 P(2) = 3500(0.97) people P(2) P(1) The population changes by the same factor over each 1 year interval. b. P(2) P(0) = P(3) = 3500(0.97) people P(3) P(1) The population changes by the same factor over each 2 year interval. a. 1 point for the factor between 2000 and 2001; 1 point for the factor between 2001 and 2002; 1 point for work b. 1 point for the factor between 2000 and 2002; 1 point for the factor between 2001 and 2003; 1 point for work Algebra 1 Teacher Guide 59 Common Core Assessment Readiness

68 F.LE.1b* Answers 1. B 2. B 3. B, D, E 4. h(x) changes at a constant rate per unit change in x = = = = 6 The function values decrease by 6 per unit change in x. 1 point for answer; 2 points for explanation using function values 5. Yes, Samantha s hourly pay grows at a rate of $0.25 per hour each month. The increase is always the same, so her pay increases at a constant rate per unit change in month. 1 point for answer; 1 point for explanation 6. 4 miles = 2 miles per hour; 2 hours 1.5 miles 1.5 miles = = 2 miles per hour 45 minutes 3 4 hour They hike at the same rate over both intervals, so they hike at a constant rate of 2 miles per hour. 1 point for answer; 1 point for unit rate 7. a. Tim s base pay increases by $1000 after the first year and by $1040 after the second year, so it does not change at a constant rate. b. Tim s commission rate increases by 1.5% after the first year and increases by 1.5% again after the second year, so it changes at a constant rate. a. 1 point for answer; 0.5 point for explanation b. 1 point for answer; 0.5 point for explanation 8. a. Year Company A Company B b. Company B s workforce has a constant rate of growth per unit change in year. Company A: = = = 60 Company B: = = = 50 c = 700 workers a. 0.5 point for each value b. 1 point for Company A s workforce; 1 point for Company B s workforce; 1 point for correct conclusion c. 1 point Algebra 1 Teacher Guide 60 Common Core Assessment Readiness

69 F.LE.1c* Answers 1. C 2. C 3. A, C 4. f(x) changes at a constant factor per unit change in x = 1 4, = 1 4, 8 32 = 1 4, and 2 8 = 1 4 The function values of f(x) change by a factor of 1 per unit change in x. 4 1 point for answer; 2 points for explanation 5. Yes; the decay factor for each year is 0.5, which can be written as in the form 1 r, where r is the decay rate per year. So, the number of nests decreases by 50% each year. 1 point for answer; 2 points for explanation 6. Yes; , , and The decay factor can be written as in the form 1 r, where r is the decay rate per minute. The decay rate as a percent is 3.35%. 1 point for answer; 1 point for decay factor; 1 point for showing work 7. The antique toy and the antique chair have values that grow by a constant factor relative to time. Antique toy: = 1.1, = 1.1, and = 1.1 Antique chair: = 1.08, = 1.08, and The value of the antique toy increases at a faster rate because the value of the antique toy grows by a factor of 1.1 per year and the value of the antique chair grows by a factor of 1.08 per year. 1 point for identifying the antiques that show constant rates; 1 point for explanation with supporting work; 1 point for stating that the value of the antique toy increases at a faster rate; 1 point for explanation 8. a. Yes; Company A: 126, ,300 = 1.05, = 1.05, and 120, , , ,300 = 1.05 Since the growth factor is 1.05, the growth rate is 0.05, so the number of visits company A s website receives grows by 5% per month. b. No; Company B: 153, ,590 = 1.02, = 1.03, and 150, , , , Since the growth factor is not the same between each month, the number of visits for company B s website does not grow by a constant percent per month. a. 1 point for answer; 2 points for explanation b. 1 point for answer; 2 points for explanation Algebra 1 Teacher Guide 61 Common Core Assessment Readiness

70 F.LE.2* Answers 1. B, C 2. C 3. D 4. B 1 = 100(1.0025) t B 2 = t 1 point for each function 5. a. Exponential. The population each day is 25% greater than the population on the previous day. b. P(t) = 1000(1.25) t a. 1 point for answer; 1 point for explanation b. 1 point 6. r = = 0.9 V(t) = a(0.9) t 18 = a(0.9) 0 18 = a V(t) = 18(0.9) t 1 point for answer; 2 points for work 7. s 5 = 36, s 12 = 64 d = = 28 7 = 4 s n = s 1 + d(n 1) 64 = s 1 + 4(12 1) 64 = s = s 1 s n = (n 1) 1 point for correct sequence; 2 points for work a. m = = = 9 y = mx + b 60 = 9(20) + b 60 = b 120 = b The art club s profit is modeled by the function P(c) = 9c 120. b. The slope is 9, which means that each comic book costs $9. The P-intercept is 120, which could mean that the art club spends $120 on supplies to make the comic books. c. The art club needs to sell 55 comic books to make $ = 9c = 9c 55 = c a. 1 point b. 1 point for interpretation of slope; 1 point for interpretation of intercept c. 1 point for answer; 1 point for work 9. a. Geometric. The ratio of consecutive distances is b. d(n) = d(1) i (0.944) n 1 = i (0.944) n 1 c. d(n) = 36.35i(0.944) n 1 d(20) = 36.35i(0.944) 20 1 = 36.35i(0.944) The 20th fret is about mm from the 19th fret. a. 1 point for answer; 1 point for ratio b. 1 point for answer; 1 point for work c. 1 point for answer; 1 point for work Algebra 1 Teacher Guide 62 Common Core Assessment Readiness

71 F.LE.3* Answers 1. A, B, E 2. C 3. C 4. a. A(t) < B(t) b. A(t) < B(t) c. A(t) > B(t) d. A(t) > B(t) e. A(t) > B(t) 5. a. A(t) = 300t B(t) = 1500(1.15) t b. Time, t (years) Town A population, A(t) Town B population, B(t) c. Town B will have a larger population than town A. A increases by the same amount (300) each year. B increases by the same percent (15%) each year. 15% of 4589 is about 688, so B will continue to increase by a greater amount than A each year after a. 1 point for each function b. 0.5 point for each value calculated c. 1 point for answer; 1 point for explanation 6. a. b. c. Initially, the values of h(x) are less than the values of f(x), but greater than the values of g(x). Eventually, the values of h(x) exceed the values of both f(x) and g(x). d. The value of an exponential function may start out less than the values of a linear function or a polynomial function for the same inputs. As x increases, the value of the exponential function will eventually be greater than the values of the linear and polynomial functions for the same inputs. a. 0.5 point for graphing each function b. 0.5 point for graphing each function c. 2 points for accurate comparison d. 2 points for accurate conjecture Algebra 1 Teacher Guide 63 Common Core Assessment Readiness