1. 2.5 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… 1.Find the vertex 2.Write two linear equations and find slope 3.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 + 12| m = -b = c =

9. Absolute Value Functions Step 1: Find the vertex y = |3x + 12| m = 3 -b = -12 c = 0

10. Absolute Value Functions Step 1: Find the vertex y = |3x + 12| m = 3 -b = -12 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| PositiveNegative

13. Absolute Value Functions Step 2: Write two linear equations and find slope. y = |3x + 12| PositiveNegative y = 3x + 12 y = -3x – 12 m 1 = m 2 =

14. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-4, 0) m 1 = 3 m 2 = -3

15. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-4, 0) m 1 = 3 m 2 = -3

16. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-4, 0) m 1 = 3 m 2 = -3

17. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-4, 0) m 1 = 3 m 2 = -3

18. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-4, 0) m 1 = 3 m 2 = -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 PositiveNegative

24. Absolute Value Functions Step 2:Write two linear equations and find slope y = |3x + 6| - 2 Positive Negative y + 2 = 3x + 6 y + 2 = -3x – 6 y = 3x + 4 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 + 6 y + 2 = -3x – 6 y = 3x + 4 y = -3x – 8 m= 3m= -3

26. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

27. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

28. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

29. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

30. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

31. Absolute Value Functions Step 3: Use the slope to plot points vertex = (-2, -2) m 1 = -3 m 2 = 3

32. Homework p.90 #3-5, 23-24, 29-32, 36, 39, 51 Graph each equation. 3) y = |4x – 1| 4) y = |-3x| 5) y = |-3x| + 2 23) y = |2x + 1| 24) y = 3|3x – 1| 2