1. Is the graph an increasing or decreasing function? Explain your answer.

Transcription

1 Evaluate the expression Using a graphing calculator, graph the function f(x) = 2 x and sketch the graph on the grid provided below. 1. Is the graph an increasing or decreasing function? Explain your answer Page 1

2 2. Trace or use the table feature on your calculator to fill out the tables below. As the value of x gets very large, what happens to the value of 2 x? X x As the value of x gets very small, what happens to the value of 2 x? X x. Will the value of 2 x ever equal 0? Explain your answer. 4. Are there any values of x that would make 2 x undefined? Explain your answer Without graphing, determine whether each function represents exponential growth or exponential decay. 1. y = 129(1.6) x 2. f(x) = 2(0.65) x.y = 12(17/10) x 4.y = 0.8(1/8) x 2015 Page 2

3 The number of bacteria in a culture doubles each hour. Which graph below best represents this situation? Explain your answer. A. B. C. D Page

4 1. a. The two equations below represent two different populations of Skeeters. Graph both equations on the same set of axes. When will these populations be approximately the same size? 1. y = x 2. y = 1 2x b. Find the size of each population when x = 0. What do these values represent? 2. The table below shows the population of Skeeters in a container after each of 5 shakes. Write an equation which could be used to describe this data. (Your equation may not describe the data exactly.) Shake Number Population Total Page 4

5 Simplify each Radical Expression. If necessary use absolute value signs h c 7 b. 64s Page 5

6 Simplify by combining like terms x + 5 5x 2 5x 2. 5 b 2 b + 4 b Write each expression in simplest radical form (using at most one radical sign) =. x 1 x 1 = = 4. (a 4 5 ) 5 = 2015 Page 6

7 Simplify completely. 1. 2x x 2. 2a b. 4b 2a 4. 2y x 2015 Page 7

8 Sketch the graph of each function 1. f(x) = 4 2 x 2. f(x) = 5 ( 1 2 )x 2015 Page 8

9 . y = 4 2 x 4. y = 4 ( 1 2 )x 2015 Page 9

10 Exponential Growth: Investing 1. You deposit $1500 in an account that pays 6% interest compounded yearly. Find the balance after 5 years. Equation: Balance after 5 years: 2. You deposit $500 in an account that pays 8.4% interest compounded yearly. Find the balance after 9 years. Equation: Balance after 9 years: 2015 Page 10

11 . Which option gives the greater balance? Show the balance for each option. a. Put $500 in an account that pays 7.5% interest compounded yearly for 9 years. Equation: Balance after 9 years: b. Put $700 in an account that pays 6.5% interest compounded yearly for 8 years. Equation: Balance after 8 years: Which investment is better? 2015 Page 11

12 4. Which option gives the greater balance? Show the balance for each option. a. Put $2000 in an account that pays 8% interest compounded yearly for 10 years. Equation: Balance after 10 years: b. Put $1500 in an account that pays 12% interest compounded yearly for 8 years. Equation: Balance after 8 years: Which investment is better? 2015 Page 12

13 1. Write the equation for the function that results from each transformation applied to the base function y = 5 x. a) translate down unit b) shift right 2 units c) translate left ½ unit d) shift up 1 unit and left 2.5 units 2. Describe the transformations that map the function y = 8 x onto each function. a) y = ( 1 2 ) 8x b) y = 8 4x c) y = 8 x d) y = 8 2x. Write the equation for the function that results from each transformation applied to the base function y = 7 x a) reflect in the x-axis (vertical reflection) b) stretch vertically by a factor of c) stretch horizontally by a factor of 2.4 d) reflect in the y-axis and stretch vertically by bafo 7 4. Sketch the graph of y = ( 1 2 ) 2x 4 by using y = 2 x as the base and applying transformations Page 1

14 1. Using the two given values fill in the missing numbers for a linear function and for an exponential function. a Linear 48 Exponential 48 b Linear Exponential You plan on saving money for college. You start when you are 8 years old with $500 that you earned during the summer. You plan on earning 8% per year on your investment. What is the exponential function that shows how much you will make? Complete the table and graph. How much money will you have after 5 years? 8 years? 10 years? t f(t) f(t)= f(5)= f(8)= f(10)= 2015 Page 14

15 . Fill in the function table and plot the points, connect the points in order. Show your work! x f(x) = 6 ( 1 ) x f(x) (x, f(x)) Page 15

16 Answer Key Evaluate the expression = = 4 6 = (5 2 ) = 5 2 = 5 6 = = = = = 5 = 1 = ( 7 ) = = Using a graphing calculator, graph the function f(x) = 2 x and sketch the graph on the grid provided below. 5. This is increasing graph. When a > 0 and b is greater than 1, the graph will be increasing. In our case, a = 1 and b = Trace or use the table feature on your calculator to fill out the tables below. As the value of x gets very large, what happens to the value of 2 x? X 2 x As the value of x gets very small, what happens to the value of 2 x? X 2 x Page 16

17 7. As the value of x gets very small, the value of 2 x will approach to 0, but it will never be equal to Exponential function y = 2 x is defined for all real numbers. So, it will never be undefined. Without graphing, determine whether each function represents exponential growth or exponential decay. 1. y = 129(1.6) x 2. f(x) = 2(0.65) x.y = 12(17/10) x 4.y = 0.8(1/8) x Growth Decay Growth Decay The number of bacteria in a culture doubles each hour. Which graph below best represents this situation? Explain your answer. D. Graph D is the answer. We can write this function as y = 2 x and that function represents the graph D. 1. a. The two equations below represent two different populations of Skeeters. Graph both equations on the same set of axes. When will these populations be approximately the same size? 1. y = x 2. y = 1 2x They will never be the same size Page 17

18 b. Find the size of each population when x = 0. What do these values represent? When x = 0 y1 = 10 y2 = 0 The values represent the population at start. 2. The table below shows the population of Skeeters in a container after each of 5 shakes. Write an equation which could be used to describe this data. (Your equation may not describe the data exactly.) Answer y = 2 (.5) x Simplify each Radical Expression. If necessary use absolute value signs h 2 = 2 5h c^7b = 7bc 7. 64s = 4s 4. 8 = 2 Simplify by combining like terms x 2. 7 b Write each expression in simplest radical form (using at most one radical sign) x 2 4. a 4 Simplify completely a b b. 2b 4. a 2y x2 x 2015 Page 18

19 Sketch the graph of each function 1. f(x) = 4 2 x 2. f(x) = 5 ( 1 2 )x. y = 4 2 x 4. y = 4 ( 1 2 )x 2015 Page 19

20 Exponential Growth: Investing 1. Equation: A = 1500 (1.06) t Balance after 5 years: A = $ Equation: A = 500 (1.084) t Balance after 9 years: A = $ a. Put $500 in an account that pays 7.5% interest compounded yearly for 9 years. Equation: A = 500 (1.075) t Balance after 9 years: A = $ b. Put $700 in an account that pays 6.5% interest compounded yearly for 8 years. Equation: A = 700 (1.065) t Balance after 8 years: A = $ Second investment (option B) is better. Which option gives the greater balance? Show the balance for each option. a. Equation: A = 2000 (1.08) t Balance after 10 years: A = $ b. Equation: A = 1500 (1.12) t Balance after 8 years: A = #71.94 First Investment (options A) is better 2015 Page 20

21 1. Write the equation for the function that results from each transformation applied to the base function y = 5 x. a) y = 5 x b) y = 5 x 2 c) y = 5 x+1 2 d) y = 5 x Describe the transformations that map the function y = 8 x onto each function. a) Vertically shrinks the graph by 1 2 b) Horizontally shrinks the graph by 4. c) Reflects the graph about x-axis d) Horizontally shrinks the graph by 2 and reflect the graph about y-axis. Write the equation for the function that results from each transformation applied to the base function y = 7 x a) y = (7) x b) y = (7) x c) y = (7) 2.4x d) y = 7 (7) x 4. Sketch the graph of y = ( 1 2 ) 2x 4 by using y = 2 x as the base and applying transformations Page 21

22 1. Using the two given values fill in the missing numbers for a linear function and for an exponential function. a Linear Exponential b Linear Exponential f(t) = t t f(t) f(t)= t f(5)= f(8)= f(10)= Page 22

23 . Fill in the function table and plot the points, connect the points in order. Show your work! x f(x) = 6 ( 1 ) x f(x) (x, f(x)) f(x) = 6 ( 1 ) 1 18 ( 1, 18) f(x) = 6 ( 1 ) 0 6 (0, 6) f(x) = 6 ( 1 ) 1 2 (1, 2) f(x) = 6 ( 1 ) 2 2/ f(x) = 6 ( 1 ) 2/9 f(x) = 6 ( 1 ) 4 2/27 (2, 2 ) (, 2 9 ) (4, 2 27 ) 2015 Page 2

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