1. Unit 8 Lesson 11
Piecewise Functions

2. Let’s Review What is our domain? What is our range?
What is a function?
What is a relation?
Why is it important?

3. Remind me…Is this a function?
a. f(x)={(1,6), (2,6), (3,8), (4,9)}
b. g(x)={(6,1), (6,2), (8,3), (9,4)} c. d.

4. Wait…So what is this x and f(x)???

5. Understanding functions
A function is increasing on an interval when the slope is positive ( / )
A function is decreasing on an interval when the slope is negative ( \ )
A function is constant on an interval when there is zero slope (a straight line — )

6. IMAGES OF WHAT IT LOOKS LIKE FOR A GRAPH TO INCREASE, DECREASE, OR REMAIN CONSTANT

7. What is a piecewise function?
A Function Can be in Pieces
We can create functions that behave differently based on the input (x) value.
QUESTION: Is the input our Domain (X) or Range (Y)?
Here is a function made up of 3 pieces, they can be more or less pieces…

8. But i’m confused how to name the domain and range…

9. Let’s look at this function…
Here is an example of a piecewise function:
What is h(-1)?
It’s the same as what is h(x)=?
What is h(1)?
x is ≤ 1, so what is our output when x=1?
What is h(4)?
x is > 1, so we use h(x) = x, so h(4) = ?

10. How do we explain it? In the example:
when x is less than 2, it gives x2,
when x is exactly 2 it gives 6
when x is more than 2 and less than or equal to 6 it gives the line 10-x
**Just like INTERVAL NOTATION with inequalities: a solid dot means “including", an open dot means "not including"

11. DO WE HAVE EXTRA TIME? THEN LET’S CHECK OUT THIS SITE
range-01