1. 2.7 Use Absolute Value Functions and Transformations

2. In this lesson you will:
Represent absolute value functions.
Use absolute value function to model real-life situations.

3. The definition of Absolute Value
By the way…..is x a positive or negative number?

4. Let’s graph y = |x| x if x > 0 0 if x = 0 |x|= -x if x < 0
Vertex
Notice that the graph is symmetric in the y axis because for every point (x,y) there is a corresponding point (-x,y)

5. Let’s explore the graph y = a|x-h|+k
The graph has a vertex (h,k) and is symmetric in the line x=h.
The graph is V-shaped. It opens up if a>0 and down if a<0.
The graph is wider then the graph of y=|x| if |a|<1.
The graph is narrower that the graph of y=|x| if |a|>1.

6. Does the graph open “up” or “down”?
What are the coordinates of the vertex?

7. Does the graph open “up” or “down”?
What are the coordinates of the vertex?

8. Graph this function

9. Graph this function
Why is the graph narrower than the last one?

10. Write an equation for this graph
y = 2|x-3|+1

11. Write an equation for this graph
y = -|x+2|+3

12. Open Book to page 126 See box for transformations of general graphs
Look at example 5

13. 2.7 Extension: Piecewise Functions

14. In this lesson you will:
Represent piecewise functions.
Use piecewise functions to modal real-life quantities.

15. Sometimes functions can be defined in “pieces”…..for example:
What is f(0)? 2
What is f(4)? 6
This function has two “pieces”….one piece to the left of 2, and the other piece to the right of 2. What do you think the graph of f(x) would look like?

16. Graph this function:
This is an example of a Step Function.