1. 2.8 : Absolute Value Functions What is absolute value? What does the graph of an absolute value function look like? How do you translate an absolute value graph?

2.  | x | = x if x is positive | x | = -x if x is negative | x | = 0 if x=0 Absolute Value

3. f(x) = | x | Use a table of values to graph:

4. 1. 3. 2. 4. In pairs, graph the following functions on your calculator in the same viewing window. Record any observations.

5. y= a |x – h| + k Vertex: (h, k), graph is symmetric to the line x = h  h is horizontal shift  k is vertical shift  a tells which way the graph opens and how steep it is If a > 0, opens up If a < 0, opens down If |a| > 1, graph is narrower than y = |x| If |a|< 1, graph is wider than y = |x| Absolute Value Function

6.  Graph f(x) = | x – 2 | -3 Example

7. Examples: 1. Graph y = - | x – 1 | +12. Graph y = 2|x + 3 |

8. 1. 2. Write a piecewise function for the following graphs.

9.  Find the x value at the vertex (this is where it changes “pieces”  If the graph opens up:  If the graph opens down: To write an absolute value function as a piecewise function (y = a |x – h| + k) :

10. 1.y=2|x+1| -1 2.f(x)=|x +4| 3.g(x) = | x-2| +2 Write as a piecewise function.

11. 1.Identify vertex and point on the graph 2.Substitute h, k, x, and y, into the equation. 3.Solve for a. 4.Write the equation using a, h and k. p. 126: # 36, 38 Writing Equation from a Graph