1. Absolute Value Functions
Graphs
and
Compound Functions

2. Absolute Value Functions
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Graphs
1. Translations
Quick Graphs
Graphing Inequalities
Writing as Compound Functions
4. Using the vertex and slopes
5. From Definition

3. Absolute Value Functions
Translations

4. y =|x|

5. y = |x+1| + 2
x+1 = 0
x = -1 2 1

6. y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2

7. y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 stretch stretch Slope: 2

8. y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 stretch stretch 3/2 squeeze
Slope: -3(2) = -6
Slope: 3(2) = 6

9. Absolute Value Functions
Quick Graphs

10. y =|x|

11. y = |x+1| + 2
x+1 = 0
x = -1 2 1

12. y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2

13. y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 stretch stretch Slope: 2

14. y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 stretch stretch 3/2 squeeze
Slope: -3(2) = -6
Slope: 3(2) = 6

15. Absolute Value Functions
Graphing Inequalities

16. y ≤ |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 Where do we shade? 5/2 squeeze
Slope: -2
Slope: 2

17. y > -2 |x - 3| + 1 x - 3 = 0 x = 3 Where do we shade? 1 3 stretch
Slope: 2
Slope: -2

18. y ≥ |x+1| + 2
x+1 = 0
x = -1
Where do we shade? 2 1

19. y < -2 |3x + 4| + 1
3x + 4 = 0
x = -4/3
Where do we shade? 1
4/3
stretch
stretch
squeeze
squeeze
Slope: (2)(3) = 6
Slope: -(2)(3) = -6

20. y ≥ 3|-2x + 8| - 1 -2x + 8 = 0 x = 4 1 Where do we shade? stretch
squeeze
squeeze
squeeze
Slope: -3(2) = -6
Slope: 3(2) = 6

21. Absolute Value Functions
Writing as
Compound Functions
using
Vertex and slopes

22. y = | x + 2 | What is missing? Compound function Vertex (-2, 0)
Slopes of sides
m = ± 1
Vertex (-2, 0)
left side
right side
What is
missing?
Compound
function
Jeff Bivin -- LZHS

23. y = 3| x - 4 | What is missing? Compound function Vertex (4, 0)
Slopes of sides
m = ± 3
Vertex (4, 0)
left side
right side
What is
missing?
Compound
function

24. y = -2| x + 1 | Don't forget Compound function Vertex left side
Slopes of sides
m = ± 2
Vertex
left side
right side
Don't
forget
Compound
function

25. y = 2| x - 5 | +3 Don't forget Compound function Vertex (5, 3)
Slopes of sides
m = ± 2
Vertex (5, 3)
left side
right side
Don't
forget
Compound
function

26. y = -4| 2x - 5 | + 7 Don't forget Compound function Vertex left side
Slopes of sides
m = ± 8
Vertex
left side
right side
Don't
forget
Compound
function

27. Absolute Value Functions
Writing as
Compound Functions
From Definition

28. y = | x + 2 |
If x > -2
If x < -2

29. y = 3| x - 4 |
If x > 4
If x < 4

30. y = -2| x + 1 |
If x > -1
If x < -1

31. y = -3| 2x + 3 | + 1