ABSOLUTE VALUE FUNCTIONS
Graphsand
Compound Functions
ABSOLUTE VALUE FUNCTIONS
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Graphs1. Translations
2. Quick Graphs
3. Graphing Inequalities
Writing as Compound Functions4. Using the vertex and slopes
5. From Definition
ABSOLUTE VALUE FUNCTIONS
Translations
y =|x|
y = |x+1| + 2
y = |2x+5| - 4
y = 2 |x - 3| + 1
y = 3 |2x - 3| - 4
ABSOLUTE VALUE FUNCTIONS
Quick Graphs
y =|x|
y = |x+1| + 2
y = |2x+5| - 4
y = 2 |x - 3| + 1
y = 3 |2x - 3| - 4
ABSOLUTE VALUE FUNCTIONS
Graphing Inequalities
y ≤ |2x+5| - 4
y > -2 |x - 3| + 1
y ≥ |x+1| + 2
y < -2 |3x + 4| + 1
y ≥ 3|-2x + 8| - 1
ABSOLUTE VALUE FUNCTIONS
Writing as
Compound Functions
using
Vertex and slopes
y = | x + 2 | 02 x2x
)2(10 xy
2xy 21 xy2 xy
2,2
2,2
xx
xxy
0,2
Vertex (-2, 0)
Slopes of sides
m = ± 1
right side
1m1m
21 xy
left side
210 xy
2x2x 2x
Jeff Bivin -- LZHS
y = 3| x - 4 | 04 x4x
430 xy123 xy123 xy
4,123
4,123
xx
xxy
0,4
Vertex (4, 0)
Slopes of sides
m = ± 3
right side
3m3m
left side
430 xy
4x4x 4x
y = -2| x + 1 | 01x1x
)1(20 xy 12 xy
22 xy
1,22
1,22
xx
xxy
0,1
Vertex
Slopes of sides
m = ± 2
right side
2m2m
left side
)1(20 xy
1x1x
1x
22 xy
12 xy
0,1
y = 2| x - 5 | +3 05 x5x
523 xy1023 xy
132 xy
5,132
5,72
xx
xxy
3,5
Vertex (5, 3)
Slopes of sides
m = ± 2
right side
2m2m
left side
523 xy
5x5x 5x
72 xy
1023 xy
y = -4| 2x - 5 | + 7 052 x52 x
2587 xy2087 xy
138 xy
25
25
,138
,278
xx
xxy
7,25
Vertex
Slopes of sides
m = ± 8
right side
8m8m
left side
2587 xy
25x
25x
25x
278 xy
2087 xy
25x
7,25
ABSOLUTE VALUE FUNCTIONS
Writing as
Compound Functions
From Definition
y = | x + 2 |
02 x
2x
If x > -2
2 xy
2xy
If x < -2
2 xy
2 xy
2,2
2,2
xx
xxy
2x
y = 3| x - 4 |
04 x
4x
If x > 4
43 xy
123 xy
If x < 4
43 xy
123 xy
4,123
4,123
xx
xxy
4x
y = -2| x + 1 |
01x
1xIf x > -1
12 xy
22 xy
If x < -1
12 xy
22 xy
4,22
1,22
xx
xxy
2x
y = -3| 2x + 3 | + 1
032 x32 x 1323 xy
196 xy 132)3( xy
1)32(3 xy
23
23
,106
,86
xx
xxy
23x
23x
23xIf 2
3xIf
86 xy 196 xy106 xy
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