1. Trinity claims that the graph of the function g(x) = ƒ(x k) is located k units to the right of the graph of ƒ(x).

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1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra I Benchmark 1 Description: Algebra 1 Topics 3 and 4 Test Form: Trinity claims that the graph of the function g(x) = ƒ(x k) is located k units to the right of the graph of ƒ(x). Which statement best describes Trinity's claim? The claim is never true, since the graph of ƒ(x) is shifted up or down by k units. The claim is always true, since any value of k will shift the graph of ƒ(x) to the right. The claim is only true for k 0, since positive values of k will shift the graph of ƒ(x) to the left. The claim is only true for k 0, since negative values of k will shift the graph of ƒ(x) to the left.

2 2. An equation is represented by the graph below. Which of the following ordered pairs is most likely a solution to the equation represented by the graph? (2, 0) (5, 2) (6, 10) (10, 2)

3 3. The graph of the function and the transformed graph are shown below. What is the value of k?

4 4. During a recent snowstorm, John measured the total snowfall accumulated at the end of each hour. He recorded his results in the table below. What is the approximate average rate of change of the snowfall between 1 p.m. and 6 p.m.? 0.7 inch/hour 0.9 inch/hour 1.1 inches/hour 1.4 inches/hour

5 5. The table below provides the values of the functions x. for several values of Which of the following is a solution to the equation

6 6. Two different functions are shown below. One is written as an equation, and the other is given as a table of values. Which mathematical sentence correctly compares the y-intercept of function A to the y-intercept of function B?

7 7. Rosa is filling up the back of her dump truck with cedar mulch for a delivery to a landscaped shopping center. The mulch is being pumped into the truck. After 30 minutes, the truck is 75% full and weighs 33 tons. Fifteen minutes later, Rosa's truck is fully loaded and weighs 42 tons. If Rosa's truck weighs 15 tons when it is empty, what was the rate in tons per minute that the mulch pump took to load the truck? 0.6 tons per minute 0.93 tons per minute 1.07 tons per minute 1.67 tons per minute 8. If a point is on the graph of the equation and also on the graph of what is the value of b?

8 9. A dance department is planning a holiday show. The department needs to raise at least $450 in order to cover the cost of costumes and decorations. Tickets will be sold at $5 for adults and $3 for students. Let a represent the number of adult tickets and s represent the number of student tickets. Which inequality should be used to represent the number of tickets that must be sold in order to raise the amount of money needed for the show?

9 10. The table below shows some inputs and outputs of function f(x). Which statement best describes the function? f(x) is a linear function because x is doubling in each row of the table. f(x) is an exponential function because x is doubling in each row of the table. f(x) is a linear function because f(x) is increasing by 4 for each increase in x by 1. f(x) is an exponential function because f(x) is increasing by 4 for each increase in x by 1.

10 11. The value of a certain house is modeled by the function where x represents the number of years since it was bought. Which statement is true? The initial cost of the house is $2,500. The value of the house will increase to $126,000 over a period of time. The initial cost of the house is $126,000, and the value is decreasing by $2,500 every year. The initial cost of the house is $126,000, and the value is increasing by $2,500 every year. 12. A table of values for the equation y = f(x) contains an x value of 6 and a corresponding y value of 12, as does a table of values for the equation y = g(x). Which of these must be solution to the equation f(x) = g(x)? x = 6 x = 12 Both x = 6 and x = 12 Neither x = 6 nor x = 12

11 13. A school is collecting canned food as a service project. There are 30 classes participating in the project. The goal is to collect more than 1,000 canned food items. If each class collects the same number of cans, what is the least number of cans each class must collect to meet the goal? An arithmetic sequence is defined as follows: A student draws a graph with points at for all values of What is the slope of the graph?

12 15. In order to lure new customers to a credit card, a bank is offering an initial cash back award, plus cash back amounting to a percentage of the value of all purchases made with the card. If p is the value of all purchases made with the card and c is the amount of cash back, which of these equations does the graph represent? c = 0.03p c = 0.3p c = 1.03p c = 1.3p A hiker is at a height of 700 meters and begins her descent. She descends at a rate of 13m/min. Which function rule describes the climber's height of elevation after t minutes? H(t)= 700t - 13 H(t)= 700t + 13 H(t)= 700(13t) H(t)= t

13 17. As a part of a science experiment, Gary makes a small hole in the bottom of a bottle full of water. He records the amount of water left in the bottle at the end of each minute. He repeats this experiment several times and uses the data to develop the linear model which describes the amount of water remaining in the water bottle, in w milliliters, after m minutes. Which statement is a correct interpretation of this linear model? The water bottle holds 1,200 milliliters of water and loses 50 milliliters per minute. The water bottle starts with 1,200 milliliters of water and ends with 24 milliliters of water. The water bottle holds 1,200 milliliters of water and loses 1 milliliter of water every 50 minutes. The water bottle starts with 1,200 milliliters of water and loses exactly 50 milliliters of water. 18. The cost of a notebook, x, is twice the cost of a pen, y. Which equation can be used to represent this relationship?

14 19. Which of the following graphs represent a function of the form y = a x + 1 for some real number a? Select two that apply.

15 E. 20. Carla invests $3000 in a family fund that pays 5% interest every year, but only on her principal investment. The formula the fund uses to calculate the amount in her account, A, based on the number of years, t, since she invested the $3000 is shown below. Which statement is true about the amount in Carla's account over time? The amount in Carla's account increases by a factor of 0.05 each year. The amount in Carla's account increases by a factor of 1.05 each year. The amount in Carla's account increases by $150 each year. The amount in Carla's account increases by $3150 each year.

16 21. Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? C(t) = 0.10t + 25 C(t) = 0.10t + 25 C(t) = 25(0.10) t C(t) = 25( ) t

17 22. Which inequality does the shaded region of the graph represent? y 4x y 1 4 x y 4x y 1 4 x

18 23. What is the y-intercept of the function shown on the coordinate plane below?

19 24. The graph of a linear function is shown below. Which of these statements correctly compares the graphed function function to the The rate of change of The rate of change of The rate of change of The rate of change of

20 25. In order for Josh to graph the solution to the inequality 4x 2y > 6, which of the following steps could he use to graph the inequality? Select three that apply. Rewrite the inequality as y > 2x 3. Rewrite the inequality as y < 2x 3. Draw the line y = 2x 3 as a dashed line. Draw the line y = 2x 3 as a solid line. E. Shade above the line. F. Shade below the line.

21 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra I Benchmark 1 Description: Algebra 1 Topics 3 and 4 Test Form: Trinity claims that the graph of the function g(x) = ƒ(x k) is located k units to the right of the graph of ƒ(x). Which statement best describes Trinity's claim? MAFS.912.F-BF.2.3 Webb: 3 The claim is never true, since the graph of ƒ(x) is shifted up or down by k units. The claim is always true, since any value of k will shift the graph of ƒ(x) to the right. The claim is only true for k 0, since positive values of k will shift the graph of ƒ(x) to the left. The claim is only true for k 0, since negative values of k will shift the graph of ƒ(x) to the left.

22 2. An equation is represented by the graph below. Which of the following ordered pairs is most likely a solution to the equation represented by the graph? MAFS.912.A-REI.4.10 Webb: 1 (2, 0) (5, 2) (6, 10) (10, 2)

23 3. The graph of the function and the transformed graph are shown below. What is the value of k? MAFS.912.F-BF.2.3 Webb: 2

24 4. During a recent snowstorm, John measured the total snowfall accumulated at the end of each hour. He recorded his results in the table below. What is the approximate average rate of change of the snowfall between 1 p.m. and 6 p.m.? MAFS.912.F-IF.2.6 Webb: inch/hour 0.9 inch/hour 1.1 inches/hour 1.4 inches/hour

25 5. The table below provides the values of the functions x. for several values of Which of the following is a solution to the equation MAFS.912.A-REI.4.11 Webb: 1

26 6. Two different functions are shown below. One is written as an equation, and the other is given as a table of values. Which mathematical sentence correctly compares the y-intercept of function A to the y-intercept of function B? MAFS.912.F-IF.3.9 Webb: 1

27 7. Rosa is filling up the back of her dump truck with cedar mulch for a delivery to a landscaped shopping center. The mulch is being pumped into the truck. After 30 minutes, the truck is 75% full and weighs 33 tons. Fifteen minutes later, Rosa's truck is fully loaded and weighs 42 tons. If Rosa's truck weighs 15 tons when it is empty, what was the rate in tons per minute that the mulch pump took to load the truck? MAFS.912.F-IF.2.6 Webb: tons per minute 0.93 tons per minute 1.07 tons per minute 1.67 tons per minute 8. If a point is on the graph of the equation and also on the graph of what is the value of b? MAFS.912.A-REI.4.10 Webb: 1

28 9. A dance department is planning a holiday show. The department needs to raise at least $450 in order to cover the cost of costumes and decorations. Tickets will be sold at $5 for adults and $3 for students. Let a represent the number of adult tickets and s represent the number of student tickets. Which inequality should be used to represent the number of tickets that must be sold in order to raise the amount of money needed for the show? MAFS.912.A-CE1.3 Webb: 2

29 10. The table below shows some inputs and outputs of function f(x). Which statement best describes the function? MAFS.912.F-LE.1.1.a Webb: 1 f(x) is a linear function because x is doubling in each row of the table. f(x) is an exponential function because x is doubling in each row of the table. f(x) is a linear function because f(x) is increasing by 4 for each increase in x by 1. f(x) is an exponential function because f(x) is increasing by 4 for each increase in x by 1.

30 11. The value of a certain house is modeled by the function where x represents the number of years since it was bought. Which statement is true? MAFS.912.F-LE.2.5 Webb: 1 The initial cost of the house is $2,500. The value of the house will increase to $126,000 over a period of time. The initial cost of the house is $126,000, and the value is decreasing by $2,500 every year. The initial cost of the house is $126,000, and the value is increasing by $2,500 every year. 12. A table of values for the equation y = f(x) contains an x value of 6 and a corresponding y value of 12, as does a table of values for the equation y = g(x). Which of these must be solution to the equation f(x) = g(x)? MAFS.912.A-REI.4.11 Webb: 1 x = 6 x = 12 Both x = 6 and x = 12 Neither x = 6 nor x = 12

31 13. A school is collecting canned food as a service project. There are 30 classes participating in the project. The goal is to collect more than 1,000 canned food items. If each class collects the same number of cans, what is the least number of cans each class must collect to meet the goal? MAFS.912.A-CE1.3 Webb:

32 14. An arithmetic sequence is defined as follows: A student draws a graph with points at for all values of What is the slope of the graph? MAFS.912.F-LE.2.5 Webb: 2

33 15. In order to lure new customers to a credit card, a bank is offering an initial cash back award, plus cash back amounting to a percentage of the value of all purchases made with the card. If p is the value of all purchases made with the card and c is the amount of cash back, which of these equations does the graph represent? MAFS.912.A-CE1.2 Webb: 1 c = 0.03p c = 0.3p c = 1.03p c = 1.3p A hiker is at a height of 700 meters and begins her descent. She descends at a rate of 13m/min. Which function rule describes the climber's height of elevation after t minutes? MAFS.912.F-LE.1.2 Webb: 1 H(t)= 700t - 13 H(t)= 700t + 13 H(t)= 700(13t) H(t)= t

34 17. As a part of a science experiment, Gary makes a small hole in the bottom of a bottle full of water. He records the amount of water left in the bottle at the end of each minute. He repeats this experiment several times and uses the data to develop the linear model which describes the amount of water remaining in the water bottle, in w milliliters, after m minutes. Which statement is a correct interpretation of this linear model? MAFS.912.S-I3.7 Webb: 2 The water bottle holds 1,200 milliliters of water and loses 50 milliliters per minute. The water bottle starts with 1,200 milliliters of water and ends with 24 milliliters of water. The water bottle holds 1,200 milliliters of water and loses 1 milliliter of water every 50 minutes. The water bottle starts with 1,200 milliliters of water and loses exactly 50 milliliters of water. 18. The cost of a notebook, x, is twice the cost of a pen, y. Which equation can be used to represent this relationship? MAFS.912.A-CE1.2 Webb: 2

35 19. Which of the following graphs represent a function of the form y = a x + 1 for some real number a? Select two that apply. MAFS.912.F-IF.3.7.a Webb: 2

36 E. 20. Carla invests $3000 in a family fund that pays 5% interest every year, but only on her principal investment. The formula the fund uses to calculate the amount in her account, A, based on the number of years, t, since she invested the $3000 is shown below. Which statement is true about the amount in Carla's account over time? MAFS.912.F-LE.1.1.a Webb: 2 The amount in Carla's account increases by a factor of 0.05 each year. The amount in Carla's account increases by a factor of 1.05 each year. The amount in Carla's account increases by $150 each year. The amount in Carla's account increases by $3150 each year.

37 21. Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? MAFS.912.F-LE.1.2 Webb: 2 C(t) = 0.10t + 25 C(t) = 0.10t + 25 C(t) = 25(0.10) t C(t) = 25( ) t

38 22. Which inequality does the shaded region of the graph represent? MAFS.912.A-REI.4.12 Webb: (None) y 4x y 1 4 x y 4x y 1 4 x

39 23. What is the y-intercept of the function shown on the coordinate plane below? MAFS.912.F-IF.3.7.a Webb: 1

40 24. The graph of a linear function is shown below. Which of these statements correctly compares the graphed function function to the MAFS.912.F-IF.3.9 Webb: 1 The rate of change of The rate of change of The rate of change of The rate of change of

41 25. In order for Josh to graph the solution to the inequality 4x 2y > 6, which of the following steps could he use to graph the inequality? Select three that apply. MAFS.912.A-REI.4.12 Webb: 1 Rewrite the inequality as y > 2x 3. Rewrite the inequality as y < 2x 3. Draw the line y = 2x 3 as a dashed line. Draw the line y = 2x 3 as a solid line. E. Shade above the line. F. Shade below the line.