ExamView - 9 Functions

8/12/2019 ExamView - 9 Functions

1/16

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

garde 9 functions

Graph the function.

____ 1. y 8 1

3

x

a. c.

b. d.


2/16

Name: ________________________ ID: A

2

____ 2. y 15 3( ) x

a. c.

b. d.

____ 3. The half-life of a certain radioactive material is 71 hours. An initial amount of the material has a mass of722 kg. Write an exponential function that models the decay of this material. Find how much radioactivematerial remains after 17 hours. Round your answer to the nearest thousandth.

a. y 722 12

171

x

; 611.589 kg c. y 121

722

171

x

; 0.103 kg

b. y 2 1722

171

x

; 0.414 kg d. y 722 12

71 x

; 0 kg


3/16

Name: ________________________ ID: A

3

Graph the equation.

____ 4. y x 1

a. c.

b. d.


4/16

Name: ________________________ ID: A

4

____ 5. y 0.5 x 2 2

a. c.

b. d.

____ 6. Rewrite y 9 x 36 4 to make it easy to graph using a translation. Describe the graph.

a. y 3 x 4 4.

It is the graph of y 3 x translated 4 units right and 4 units down.

b. y x 4 4 .

It is the graph of y x translated 4 units right and 4 units down.

c. y 3 x 4 4 .

It is the graph of y 3 x translated 4 units left and 4 units down.

d. y x 4 4 . It is the graph of y x translated 4 units left and 4 units down.


5/16

Name: ________________________ ID: A

5

What function matches the graph?

____ 7.

a. f x( )

x 2, for x 1

3, for 1 x 2

32

x 4, for x 2

c. f x( )

x 2, for x 1

3, for 1 x 2

32

x 6, for x 2

b. f x( )

x 2, for x 1

3, for 1 x 2

3

2

x 6, for x 2

d. f x( )

x 2, for x 1

3, for 1 x 2

3

2

x 6, for x 2

____ 8. Write a piecewise function for the graph.

a. f x( ) 3 x 3, for x 0

3 x 3, for x 0

c. f x( ) 3 x 3, for x 0

3 x 3, for x 0

b. f x( ) 3 x 3, for x 0

3 x 3, for x 0

d. f x( ) 3 x 3, for x 0

3 x 3, for x 0


6/16

Name: ________________________ ID: A

6

____ 9. The graph of f x( )is given below. What is the graph of g x( ) f x( ) 1?

a. c.

b. d.

____ 10. f x( ) 9 x2 and g x( ) 9

9 x2. What is f g

x( ) and f

g

2( )?

a. 18 x

2

9 x2

;14

5c. x

2

9 x2

; 4

5

b. 9 9 x2 ; 9 5 d. x2 9 x2 ; 4 5


7/16

Name: ________________________ ID: A

7

____ 11. f x( ) 9 2 x and g x( ) 3 4 x. What is f g

x( ) and f g

3( )?

a. 3 2 x; 24 c. 3 2 x 3 2 x

; 120

b. 3 2 x

3 2 x

; 55 d. 3 2 x

3 2 x

; 25

12. Jake multiplied the two functions as shown.

f x( ) 7 x 4

g x( ) 7 x 4

f g

x( ) 7 x 4

7 x 4

2 7 x 4 7 x 4 7 x 16

2 7 x 16

14 x

16

Describe and correct the error.

____ 13. A manufacturer produces blankets of different sizes. The length of the blankets is given by the functionl x( ) 2 x 5 and the width is given by the function w x( ) 4 x.

What is the function that represents the area that is covered by the blanket?a. a ( x) = 6 x2 5 c. a ( x) = 6 x2 9 x

b. a ( x) = 8 x2 5 d. a ( x) = 8 x2 20 x

____ 14. The population of Huntsville can be modeled as an exponential function f x( ) 55,000 1.015( ) x , where x

is the number of years since 2000. The population of another town, Rockville, can be modeled as f x( ) 75,000 1.015( ) x .

What function represents the total population of both towns?a. f x( ) 130,000 1.015( )

2 x c. f x( ) 130,000 2.03( ) x

b. f x( ) 130,000 2.03( )2 x d. f x( ) 130,000 1.015( ) x

15. The cost of one medium pizza with t toppings at Romano Pizza Place is given by R( x) = 7.5 + 0.50 x. Thecost of the same size pizza with t toppings at Italiano Pizza Place is given by I ( x) = 13.5 + 0.70 x.

a. Write a function, in simplest form, that represents how much more a pizza with t toppings would cost atItaliano Pizza Place than at Romano Pizza Place. Show your work.

b. How much more did it cost Jake to buy a medium pizza with 4 toppings from Italiano Pizza Place?


8/16

ID: A

1

garde 9 functionsAnswer Section

1. ANS: A PTS: 1 2. ANS: B PTS: 1

3. ANS: A PTS: 1 4. ANS: D PTS: 1 5. ANS: A PTS: 1 6. ANS: A PTS: 1 7. ANS: D PTS: 1 8. ANS: A PTS: 1 9. ANS: C PTS: 1 10. ANS: C PTS: 1 11. ANS: C PTS: 1 12. ANS:

Jake made an error multiplying the power coefficients of f ( x) and g( x).7 x 7 x 7 2 x instead of 7 x 7 x 2 7 x.

The correct product is shown below. f x( ) 7 x 4

g x( ) 7 x 4

f g

x( ) 7 x 4

7 x 4

7 2 x 4 7 x 4 7 x 16

7 2 x 16

49 x 16

PTS: 1 13. ANS: D PTS: 1 14. ANS: D PTS: 1 15. ANS:

Sample Answer:a. I R( ) x( ) 13.5 0.70 x( ) 7.5 0.50 x( )

13.5 0.70 x 7.5 0.50 x

13.5 7.5( ) 0.70 0.50( ) x 6 0.20 x

b. It cost Jake $6.80 more to buy a medium pizza with 4 toppings from Italiano Pizza Place.

PTS: 1


9/16

Name: ________________________ Class: ___________________ Date: __________ ID: B

1

garde 9 functions

Graph the function.

____ 1. y 4 1

8

x

a. c.

b. d.


10/16

Name: ________________________ ID: B

2

____ 2. y 17 2( ) x

a. c.

b. d.

____ 3. The half-life of a certain radioactive material is 52 hours. An initial amount of the material has a mass of661 kg. Write an exponential function that models the decay of this material. Find how much radioactivematerial remains after 4 hours. Round your answer to the nearest thousandth.

a. y 2 1661

152

x

; 1.214 kg c. y 661 12

52 x

; 0 kg

b. y 121

661

152

x

; 0.303 kg d. y 661 12

152

x

; 626.679 kg


11/16

Name: ________________________ ID: B

3

Graph the equation.

____ 4. y x 2

a. c.

b. d.


12/16

Name: ________________________ ID: B

4

____ 5. y 0.5 x 2 3

a. c.

b. d.

____ 6. Rewrite y 9 x 27 2 to make it easy to graph using a translation. Describe the graph.

a. y 3 x 3 2.

It is the graph of y 3 x translated 3 units right and 2 units up.

b. y 3 x 3 2.

It is the graph of y 3 x translated 3 units left and 2 units up.

c. y x 3 2. It is the graph of y x translated 3 units right and 2 units up.

d. y x 3 2.

It is the graph of y x translated 3 units left and 2 units up.


13/16

Name: ________________________ ID: B

5

What function matches the graph?

____ 7.

a. f x( )

x 2, for x 1

3, for 1 x 2

32

x 4, for x 2

c. f x( )

x 2, for x 1

3, for 1 x 2

32

x 6, for x 2

b. f x( )

x 2, for x 1

3, for 1 x 2

3

2

x 6, for x 2

d. f x( )

x 2, for x 1

3, for 1 x 2

3

2

x 6, for x 2

____ 8. Write a piecewise function for the graph.

a. f x( ) 3 x 3, for x 0

3 x 3, for x 0

c. f x( ) 3 x 3, for x 0

3 x 3, for x 0

b. f x( ) 3 x 3, for x 0

3 x 3, for x 0

d. f x( ) 3 x 3, for x 0

3 x 3, for x 0


14/16

Name: ________________________ ID: B

6

____ 9. The graph of f x( )is given below. What is the graph of g x( ) f x( ) 1?

a. c.

b. d.

____ 10. f x( ) 9 x2 and g x( ) 9

9 x2. What is f g

x( ) and f

g

2( )?

a. x2 9 x2 ; 4 5 c. 9 9 x2 ; 9 5

b. 18 x2

9 x2;

14

5d.

x2

9 x2;

4

5


15/16

Name: ________________________ ID: B

7

____ 11. f x( ) 9 2 x and g x( ) 3 4 x. What is f g

x( ) and f g

3( )?

a. 3 2 x; 24 c. 3 2 x

3 2 x

; 55

b. 3 2 x 3 2 x

; 120 d. 3 2 x

3 2 x

; 25

12. Jake multiplied the two functions as shown.

f x( ) 8 x 6

g x( ) 8 x 6

f g

x( ) 8 x 6

8 x 6

2 8 x 6 8 x 6 8 x 36

2 8 x 36

16 x

36

Describe and correct the error.

____ 13. A manufacturer produces blankets of different sizes. The length of the blankets is given by the functionl x( ) 4 x 5 and the width is given by the function w x( ) 8 x.

What is the function that represents the area that is covered by the blanket?a. a ( x) = 12 x2 13 x c. a ( x) = 12 x2 5

b. a ( x) = 32 x2 5 d. a ( x) = 32 x2 40 x

____ 14. The population of Huntsville can be modeled as an exponential function f x( ) 55,000 1.015( ) x , where x

is the number of years since 2000. The population of another town, Rockville, can be modeled as f x( ) 75,000 1.015( ) x .

What function represents the total population of both towns?a. f x( ) 130,000 1.015( )

2 x c. f x( ) 130,000 2.03( ) x

b. f x( ) 130,000 2.03( )2 x d. f x( ) 130,000 1.015( ) x

15. The cost of one medium pizza with t toppings at Romano Pizza Place is given by R( x) = 7.5 + 0.45 x. Thecost of the same size pizza with t toppings at Italiano Pizza Place is given by I ( x) = 13.5 + 0.75 x.

a. Write a function, in simplest form, that represents how much more a pizza with t toppings would cost atItaliano Pizza Place than at Romano Pizza Place. Show your work.

b. How much more did it cost Jake to buy a medium pizza with 3 toppings from Italiano Pizza Place?


16/16

ID: B

1

garde 9 functionsAnswer Section

1. ANS: C PTS: 1 2. ANS: D PTS: 1

3. ANS: D PTS: 1 4. ANS: A PTS: 1 5. ANS: C PTS: 1 6. ANS: B PTS: 1 7. ANS: C PTS: 1 8. ANS: B PTS: 1 9. ANS: C PTS: 1 10. ANS: D PTS: 1 11. ANS: B PTS: 1 12. ANS:

Jake made an error multiplying the power coefficients of f ( x) and g( x).8 x 8 x 8 2 x instead of 8 x 8 x 2 8 x.

The correct product is shown below. f x( ) 8 x 6

g x( ) 8 x 6

f g

x( ) 8 x 6

8 x 6

8 2 x 6 8 x 6 8 x 36

8 2 x 36

64 x 36

PTS: 1 13. ANS: D PTS: 1 14. ANS: D PTS: 1 15. ANS:

Sample Answer:a. I R( ) x( ) 13.5 0.75 x( ) 7.5 0.45 x( )

13.5 0.75 x 7.5 0.45 x

13.5 7.5( ) 0.75 0.45( ) x 6 0.30 x

b. It cost Jake $6.90 more to buy a medium pizza with 3 toppings from Italiano Pizza Place.

PTS: 1

Documents

ExamView - 9 Functions