College algebra test and test review

Test Two Review Name:

SHOW ALL WORK!!!

Problems 1-5. Find the intercepts. Write intercepts as ordered pairs.

1) 2 2

4x y  2) 2

9y x 

3) 3y x  4) 2

4 60y x x   5) 2 3y x 

Problems 6-7. Graph the circle. Label at least four points.

6) 2 2

( 3) ( 2) 9x y    7) 2 2

( 5) ( 4) 16x y   

Problems 8-11. Write equation of the circle described.

8) Center (4,-5); radius 7 9) Center (-1,5); through (4,7)

10) Endpoints of diameter are (7,10) and (9,-4) 11) Endpoints of diameter are (-10,12) and (8,-2)

Problems 12-14. Use the functions defined below to evaluate.

2 ( ) 2 3 1f x x x  

3 1 ( )

1

x g x

x

 



5, 3 ( )

3, 3

x h x

x x

   

  

12) ( 2)f  13) ( 5)h  14) (2)g

Problems 15-16. Write equation of the graph pictured.

15)

16)

Problems 17-20. Find domain, write in interval notation.

17) 3

( ) 7

x f x

  18

3

2

1 ( )

7 30

x g x

x x

 

 

19) 2

3 ( )

2 22 60

x h x

x x

 

  20)

3

2 ( )

9

x f x

x x

  



Problems 21-23. Determine if the function is even, odd, or neither. Show work.

21) 4 2

( ) 3f x x x   22) 5

( ) 3g x x x   23) 3

( )h x x x 

Problems 24-25. A function is given. Determine the average rate of change of the function between

the given values of the variable.

24) 2

( ) 2 ; 2, 4h t t t t t     25) 1

( ) ; 2, 3 1

g x x x x

   

Problems 26-31. Sketch the graph. Label at least three points.

26) 21

( ) ( 2) 4 2

f x x    27) ( ) 3 2 3g x x   

28) 3( ) 2 1 4h x x    29) ( ) 2 3 2f x x   

Problems 45-46. Sketch the graph. Be neat.

30)

4, 4

( ) 3, 4 4

2 8, 4

x x

g x x

x x

    

      

31)

2 6, 4

( ) 1 3, 4

2

x x

f x x x

  

   



Problems 32-35. Use the functions defined below to perform the indicated operation, simplify, and

determine the domain of the resulting function.

2 ( )f x

x 

3 ( )

1 g x

x 

 3( ) 1h x x  

2 ( ) 4d x x 

2 ( ) 2 5t x x  

32) ( )( )f g x 33) ( ) g

x f

     

34) ( )( )h d x 35) ( )( )f d x

Problem 36. Let 2

( ) 7f x x  and ( ) 2g x x  . Evaluate.

36a) ( )(3)g f 36b) ( )( )f g x

Problems 37-39. Determine if the function is one-to-one.

37) 2

( ) 10.75(5 ) 47f x x    38) 3( ) 22 37g x x  39) ( ) 42 99 8h x x   

Problems 40-43. Find the inverse function.

40) ( ) 3 2f x x  41) 5

( ) 4

x g x

 

42) 5

( ) 1

x h x

x

 

 43) 3( ) 2f x x 

44) Use the functions defined below to answer the following questions.

a) Is f(x) one-to-one?

b) Is g(x) one-to-one?

c) Does f(x) have an inverse function? Explain why or why not.

d) Complete the following table.

45) 2 ( 2) 11f x   is the graph of ( )f x reflected over the ________________ , stretched ____________

by a factor of 2, shifted ____________________ 2 units and shifted ___________________ 11 units.

Problem 46. Use the graph of f(x) below to graph the described transformation.

x f(x)

1 5

3 8

7 -2

-2 8

x g(x)

1 1

5 2

9 3

-10 -7

x 𝑔−1(𝑥)

3

2

1

-7

( )f x ( 2) 3f x  

47) Use the graph below to answer the questions.

Function?____________ f(1)=__________

One-to-One?_________ f(-2)=_________

Domain: ____________ Range: ________

Where is f(x) increasing? ____________ Where is f(x) decreasing?_______________

Intercepts: ____________________________________________

For what values of x does f(x)=1?

Are there any absolute extrema? If so, describe.

48) Use the graph below to answer the following questions.

Function? ____________

Domain: ____________

Range: ____________

49) Use the graph below to answer the following questions.

Function? ________ F(-2)=__________

Domain: ________ Where is F increasing? ________________

Range: ________ Where is F decreasing? ________________

50) Use the graph below to answer the following questions.

Function? ___________ Domain: ___________ Range: ___________

f(-2)=_______________ f(4)=______________ f(2.46)=__________

Intercepts: _____________________________________________________________

Where is f increasing? ________________________

Where is f decreasing? ________________________

Local Maximum(s): __________________________

Local Minimum(s): ___________________________

Are there any absolute extrema? If so, describe.

For what values of x does f(x)=0?

51) Use the graph below to answer the following questions.

Function? __________ f(0) = ____________

Domain: __________ Intercepts: ____________

Range: __________ ____________

For what values of x does f(x)=-1?

Where is f increasing? Use interval notation.

Where is f decreasing? Use interval notation.

Local minimums: ___________________

Local maximums: ___________________

Are there any absolute extrema? If so, describe.