NAME: _________________________________________ DUE: _________
Algebra2: REVIEW FOR ABSOLUTE VALUE TEST
1. Write the equation of an absolute value function that opens down, has a dilation, and a vertex
at (-5, 3).
2. Write the equation of an absolute value function that opens up, has a vertex at (1,1) and goes
through the point (4, 3). Does this function have a dilation or is it standard?
3. When is the vertex of an absolute value function a MAXIMUM?
4. When is the vertex of an absolute value function a MINIMUM?
5. What are the two most important characteristics about an absolute value function when
graphing it?
Solve and graph on the number line.
6.
–5x – 6 < 19
7.
3x + 9 ≥ 12
or
7 – 2x > 3
8.
-10  3x + 5 < 14
9.
3 
p
0
2
Solve the absolute value equations and graph the solutions.
11. |x – 3| = 10
x 17
10.
12.
3 x  2 33
13.
1
x  6 5
4
14.
|3x + 1| – 5 = −3
15.
–2 |x + 7| – 5 = 15
16.
 3x  3 7 2
17.
|x – 10| = –20
18.
|2x + 12| = 4x
19.
−3|x + 24| = −6x
Solve and graph the inequalities.
20. |3x + 4| ≥ 2
22.
24.
21.
3x  4  3  5
23.
2
x 5 5
3
2|5 + 2x| – 7 ≥ 15
3 4x  7 12   3
25.
1
x 1  7
3
26.
|3x + 1|+ 2 < 8
27.
–½ |3x + 2| – 1 > –5
28.
Function
A.
y = – 2|x – 1| + 7
B.
y = – ½ |x| + 3
C.
y = 5|x – 9|
D.
y = ¼ |x + 2| – 112
E.
y = –|x – 10| – 6
Direction
Write the equation.
29.
____________________________
Vertex
Domain
Range
30.
____________________________
Dilation
Sketch the graph and identify the characteristics of the graph.
28. y  x  2  4
a = ___ h = ___ k =
y 2 x  3
29.
___
a = ___ h = ___ k =
___
Vertex: _____________
Slope: _________
Vertex: _____________
Slope: _________
y-intercept: ___________________________
y-intercept: ___________________________
zeros: ________________________________
zeros: ________________________________
Domain: _____________________________
Domain: _____________________________
Range: _______________________________
Range: _______________________________
Increasing: ___________________________
Increasing: ___________________________
Decreasing: __________________________
Decreasing: __________________________
End Behavior:
As x    then f (x)  _____
As x    then f (x)  _____
End Behavior:
As x    then f (x)  _____
As x    then f (x)  _____
30.
___
y
1
x  4 1
2
a = ___ h = ___ k =
Vertex: _____________
31.
y   x 3
a = ___ h = ___ k =
___
Slope: _________
y-intercept: ___________________________
zeros: ________________________________
Vertex: _____________
Slope: _________
y-intercept: ___________________________
Domain: _____________________________
zeros: ________________________________
Range: _______________________________
Domain: _____________________________
Increasing: ___________________________
Range: _______________________________
Decreasing: __________________________
Increasing: ___________________________
End Behavior:
As x    then f (x)  _____
Decreasing: __________________________
As x    then f (x)  _____
End Behavior:
As x    then f (x)  _____
As x    then f (x)  _____
32.
33.
34.
35.