1. 9.4 Absolute Value Functions and Graphs
Graphing Absolute Value Functions

2. Absolute Value Functions
An absolute value function is a function with an absolute value as part of the equation…
f(x) = |mx + b|
Graphs of absolute value equations have two special properties:
a) a vertex
b) they look like angles

3. Absolute Value Functions
Vertex – point where the graph changes direction

4. Finding the Vertex For an equation y = |mx + b| + c, vertex = -b , c m
Example: Find the vertex of y = |4x + 2| - 3

5. Finding the Vertex For an equation y = |mx + b| + c, vertex = -b , c m
Example: Find the vertex of y = |4x + 2| - 3
Answer: = -2 , -3 4
= -1 , -3 2

6. Absolute Value Functions
Steps to graphing an absolute value function…
Find the vertex
Write two linear equations and find slope
Use slope to plot points, connect the dots

7. Absolute Value Functions
Example 1:
Graph y = |3x + 12|.

8. Absolute Value Functions
Step 1: Find the vertex
y = |3x |
m = -b = c =

9. Absolute Value Functions
Step 1: Find the vertex
y = |3x |
m = b = c = 0

10. Absolute Value Functions
Step 1: Find the vertex
y = |3x |
m = b = c = 0
vertex = -b , c m
vertex = -12 , 0 3
vertex = (-4, 0)

11. Absolute Value Functions
Step 1: Find the vertex
vertex = (-4, 0)

12. Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = |3x + 12|
Positive Negative

13. Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = |3x + 12|
Positive Negative
y = 3x y = -3x – 12
m1 = m2 =

14. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = 3
m2 = -3

15. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = 3
m2 = -3

16. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = 3
m2 = -3

17. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = 3
m2 = -3

18. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = 3
m2 = -3

19. Absolute Value Functions
Example 2:
Graph y = |3x + 6| - 2

20. Absolute Value Functions
Step 1: Find the vertex
y = |3x + 6| - 2

21. Absolute Value Functions
Step 1: Find the vertex
y = |3x + 6| - 2
m = 3 -b = -6 c = -2
vertex = (-6/3, -2)
= (-2, -2)

22. Absolute Value Functions
Step 1: Find the vertex
vertex = (-2, -2)

23. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = |3x + 6| - 2
Positive Negative

24. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = |3x + 6| - 2
Positive Negative
y + 2 = 3x y + 2 = -3x – 6
y = 3x y = -3x – 8

25. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = |3x + 6| - 2
Positive Negative
y + 2 = 3x y + 2 = -3x – 6
y = 3x y = -3x – 8
m = m = -3

26. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

27. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

28. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

29. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

30. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

31. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3