Practice Page
Directions: Read carefully and choose the best answers.

1.
Write the equation of a translation of the function f (x) = | x | that will move the function 4 units to the left and 7 units down.    grpic1

Choose:
 
f (x) = | x - 7 | - 4
 
f (x) = | x - 7 | + 4
 
f (x) = | x + 4 | - 7
 
f (x) = | x - 4 | - 7

 

 

2.
Which equation represents the graph shown at the right?
GR2

Choose:
 
y = | x + 3 | - 4
 
y = | x - 3 | - 4
 
y = | x + 4 | - 3
 
y = | x - 4 | - 3

 

 

3.
Find the solution(s) to the system:
y = x2 + 4x - 5
y = | x + 5 |
Round answer(s) to nearest hundredth if needed.
grpic2

Choose:
 
(-5,0) only
 
(-5,0) and (2.12, 6.96)
  (0,5) and (0,-5)
  (-5,0) and (2,7)

 

 

4.
What happens to the graph of f (x) = a | x | if a changes from 2 to 1?
grpic5
Choose:
 
The graph shifts down 1 unit.
 
The graph shifts up 1 unit.
 
The graph becomes wider.
 
The graph becomes narrower.



5.
Which statement is true regarding the graph of the function
f (x) = - | x + 1 | + 5 ?
  

Choose:
 
The graph opens down.
 The vertex is at (-1,-5).
 
The vertex is at (1,5).
 The axis of symmetry is x = 1.

 

 

6.
What will happen to the graph of the parabola f (x) = x2 - x - 6 if we graph its absolute value g (x) = | x2 - x - 6 | ?
  
Choose:
 
g (x) will be the reflection of f (x) over the x-axis.
 
The negative y-values of f (x) will be reflected over the x-axis.
 
The graph of f (x) will be strictly above the x-axis.
 
The graph of g (x) will be strictly above the x-axis.

 

 

7.
For the absolute value function f (x) = | x - 4 |, the equations of the lines containing its linear components ("pieces") are:
grpic3

Choose:
 
y = x + 4 and y = x - 4
 
y = -x - 4 and y = x + 4
 
y = -x + 4 and y = x + 4
 
y = -x + 4 and y = x - 4

 

 

8.
All absolute value functions and their graphs:
  
Choose:
 
open upward
have a vertex at (0,0)
 
are symmetric
have a positive only domain

 

 

9.
An absolute value function was entered into a graphing calculator, and produced the table shown at the right. What are the coordinates of the vertex (turning point) of this absolute value function?
GR9

Choose:
 
(0,1)
(1,2)
 
(-1,0)
(-2,1)

 

 

10.
Which of the following functions will intersect the graph of:
  f (x) = | 2x | + 3 ?
grpic4

Choose:
 
y = x - 2
y = x + 2
 
y = 2x - 2
y = 2x + 3



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