5-8 Absolute-Value Functions
Name
Date
Graph the function. Identify the vertex, axis of symmetry, x- and y-intercepts,
domain, and range. Tell whether the graph opens up or down.
y |x 1| 2
Choose positive, negative, and zero values for x.
x
y |x 1| 2 2
3
2
1
0
1
0
1
2
1
0
The vertex is (1, 2).
The axis of symmetry is x 1.
The x-intercepts are 3, 1.
The y-intercept is 1.
The domain is all real numbers.
The range is y 2.
The graph opens up.
y
x
2
0
2
2
4
Identify the vertex of each of the following absolute-value functions.
(Hint: The vertex occurs where the absolute-value expression equals zero.)
1. y | x 7 |
2. y | x 9 |
|x 7| 0
x 7; y 0
(7, 0)
5. y | x | 6
(0, 6)
Copyright © by William H. Sadlier, Inc. All rights reserved.
9. y | x 3 | 6
(3, 6)
(11, 19)
(4, 0)
(10, 0)
6. y | x | 11
7. y | x | 22
8. y | x | 15
(0, 11)
(0, 22)
(0, 15)
10. y | x 8 | 16
(6, 2)
14. y | x 13 | 14
18. y | x 7 | 8
2
|
5
(23, 54)
|
15. y | x 39 | 42
5
|
7
19. y | x 6.5 |
(58, 127 )
|
Lesson 5-8, pages 138–139.
20. y | x 7.3 |
(7.3, 0)
1
|
23. y x 9 1.2
(19, 1.2)
16. y | x 26 | 51
(26, 51)
(6.5, 0)
22. y x 8 12
12. y | x 25 | 31
(25, 31)
(39, 42)
(7, 8)
21. y x 3 4
11. y | x 4 | 12
(4, 12)
(13, 14)
17. y | x 6 | 2
4. y | x 10 |
(9, 0)
(8, 16)
13. y | x 11 | 19
|
3. y | x 4 |
|
1
|
24. y x 8 2.7
(18, 2.7)
Chapter 5
125
For More Practice Go To:
Graph each absolute-value function on a separate sheet of paper.
Identify the vertex, axis of symmetry, x- and y-intercepts, domain, and
range. Tell whether the graph opens up or down. Check students’ graphs.
26. y | x 8 |
vertex: (6, 0)
axis of symmetry: x 6
x-intercept: 6; y-intercept: 6
domain: all real numbers
range: y $ 0; opens up
28. y | x | 12
27. y | x | 9
vertex: (8, 0)
axis of symmetry: x 8
x-intercept: 8; y-intercept: 8
domain: all real numbers
range: y $ 0; opens up
29. y | x | 7
vertex: (0, 12)
axis of symmetry: x 5 0
x-intercept: none; y-intercept: 12
domain: all real numbers
range: y $ 12; opens up
31. y | x 2 |
30. y | x | 5
vertex: (0, 7)
axis of symmetry: x 5 0
x-intercept: 27, 7; y-intercept: 7
domain: all real numbers
range: y # 7; opens down
32. y | x 4 |
vertex: (22, 0)
axis of symmetry: x 5 22
x-intercept: 22; y-intercept: 22
domain: all real numbers
range: y # 0; opens down
2
1
|
37. How is the graph of y | x 12 | related to
the graph of y | x |?
It is the same graph, shifted 12 units to the left.
39. Which equation has a vertex of (8, 11)?
)
1
1
|
36. y x 4 2
2 1
vertex: , 2
3 6
2
axis of symmetry: x 5 3
5
x-intercept: none; y-intercept: 6
domain: all real numbers
1
range: y # ; opens down
6
Graph and compare each function. Check students’ graphs.
(
vertex: (1.8, 2.9)
axis of symmetry: x 5 1.8
x-intercept: none; y-intercept: 4.7
domain: all real numbers
range: y $ 2.9; opens up
|
35. y x 3 6
vertex: (2.5, 1.8)
axis of symmetry: x 5 2.5
x-intercept: none; y-intercept: 4.3
domain: all real numbers
range: y $ 1.8; opens up
vertex: (0, 5)
axis of symmetry: x 5 0
x-intercept: 25, 5; y-intercept: 5
domain: all real numbers
range: y # 5; opens down
33. y | x 1.8 | 2.9
vertex: (24, 0)
axis of symmetry: x 5 24
x-intercept: 24; y-intercept: 24
domain: all real numbers
range: y # 0; opens down
|
34. y | x 2.5 | 1.8
vertex: (0, 9)
axis of symmetry: x 0
x-intercept: none; y-intercept: 9
domain: all real numbers
range: y $ 9; opens up
1 1
vertex: 2 , 2
4 2
1
axis of symmetry: x 5 2
4
3
x-intercept: none; y-intercept: 2
4
domain: all real numbers
1
range: y # 2 ; opens down
2
(
)
38. How is the graph of y | x | 8 related to
the graph of y | x |?
It is the same graph, shifted 8 units down.
40. Which vertex belongs to the equation
y | 2x 3 | 4?
2
A. y | x 8 | 11
C. y | x 8 | 11
F. ( 3 , 4)
B. y | x 8 | 11
D. y | x 8 | 11
G. (4, 2 )
126
Chapter 5
3
3
H. ( 2 , 4)
2
J. (4, 3 )
Copyright © by William H. Sadlier, Inc. All rights reserved.
25. y | x 6 |