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Test Three Review Name:

SHOW ALL WORK!!!

Problems 1-10. Write a function for the given graph.

1)

2)

3) 4)

5) 6)

7) 8)

9) 10)

Problems 11-12. Graph the line. Label at least two points.

11) ( ) 3 4f x x  12) 2

( ) 5 3

g x x  

Problems 13-17. Write the equation of the line described.

13) Slope is -3, through (0,-2)

14) Slope is 8

7 , through (-1,-2)

15) Through (1,4) and (-1,-4)

16) Through (4,-3) and perpendicular to 𝑦 = 2

3 𝑥 + 1

17) Though (5,-7) and parallel to 3𝑥 − 5𝑦 = 1

Problems 18-20. Write a function for the parabola described.

18) Vertex (0,1) and thru (2,5) 19) Vertex (-5,3) and (2,9)

20) Vertex (0,1) and thru (1,0)

Problems 21-26. Provide the requested info for the given quadratic function.

21) 2

( ) 3( 2) 5f x x    22) 2

( ) 6 8h x x x   23) 2

( ) 3 6 4f x x x  

Vertex:________________ Vertex:_________________ Vertex:_________________

A.O.S:_________________ A.O.S:__________________ A.O.S:__________________

x-intercepts:_____________ x-intercepts:______________ x-intercepts:______________

y-intercepts:_____________ y-intercepts:______________ y-intercepts:______________

Domain:________________ Domain:_________________ Domain:_________________

Range:__________________ Range:___________________ Range:___________________

24) 21

( ) ( 8) 1 4

g x x   25) 2

( ) ( 3) 2f x x    26) 2

( ) 16 48 160g x x x   

Vertex:________________ Vertex:_________________ Vertex:_________________

A.O.S:_________________ A.O.S:__________________ A.O.S:__________________

x-intercepts:_____________ x-intercepts:______________ x-intercepts:______________

y-intercepts:_____________ y-intercepts:______________ y-intercepts:______________

Domain:________________ Domain:_________________ Domain:_________________

Range:__________________ Range:___________________ Range:___________________

Problems 27-28. Sketch the graph of the quadratic function. Label the vertex and two additional

points.

27) 2

( ) 4 3f x x x    28) 2

( ) 2( 4) 3g x x  

29) Standing atop a 64-foot platform, Susan throws a softball into the air at an initial speed of 48 feet per

second. The distance above the ground ℎ at 𝑡 seconds is given by ℎ = −16𝑡2 + 48𝑡 + 64.

a) Find the height of the softball after 2 seconds.

b) When will the ball hit the ground?

c) What is the maximum height and will the softball reach its peak height?

Problems 30-37. Provide the requested info and a sketch of the function.

30) 2

( ) 4 ( 2) ( 1)f x x x x   31) 6 5 4

( ) 2f x x x x  

Leading Term & End Behavior:

y-intercept:

x-intercept & multiplicity:

Cross/Bounce:

Max. Number of Turning Points:

Leading Term & End Behavior:

y-intercept:

x-intercept & multiplicity:

Cross/Bounce:

Max. Number of Turning Points:

32) 2

( ) ( 4)( 1)f x x x   33) 5 4 3

( ) 3 6 3f x x x x  

Leading Term & End Behavior:

y-intercept:

x-intercept & multiplicity:

Cross/Bounce:

Max. Number of Turning Points:

Leading Term & End Behavior:

y-intercept:

x-intercept & multiplicity:

Cross/Bounce:

Max. Number of Turning Points:

34)

2

3 2

1 ( )

9 14

x f x

x x x

 

  35)

2 2( 1)( 2)

( ) ( 2)( 3)( 5)

x x g x

x x x

  

  

Domain:

Holes:

Vertical Asymptotes (Even/Odd

Multiplicity):

Horizontal Asymptote:

x-intercepts (cross/bounce):

y-intercept:

Domain:

Holes:

Vertical Asymptotes (Even/Odd

Multiplicity):

Horizontal Asymptote:

x-intercepts (cross/bounce):

y-intercept:

36) 2

( 1)( 3)( 5) ( )

( 2) ( 4)

x x x f x

x x

   

  37)

2 3( 2) ( 5)

( ) 2( 3)( 1)( 4)

x x f x

x x x

  

  

Domain:

Holes:

Vertical Asymptotes (Even/Odd

Multiplicity):

Horizontal Asymptote:

x-intercepts (cross/bounce):

y-intercept:

Domain:

Holes:

Vertical Asymptotes (Even/Odd

Multiplicity):

Horizontal Asymptote:

x-intercepts (cross/bounce):

y-intercept: