1. Piecewise Functions

2. Evaluating Piecewise Functions
Piecewise functions are functions defined by at least two equations, each of which applies to a different part of the domain
A piecewise function looks like this:
Domain restrictions
Equations

3. Steps to Evaluate Piecewise Functions
Look at the domain (x-value) to see which equation to use
Plug in the x-value
Solve!

4. One equation gives the value of f(x) And the other when x > 1

5. Evaluate f(x) when x = 0, x = 2, x = 4
First you have to figure out which equation to use. The equations must be written so that no value of x fits more than one equation.
x = 4
x = 2
x = 0
This one fits
into the top
equation
So:
0 + 2 = 2
f(0) = 2
So:
2(2) + 1 = 5
f(2) = 5
So:
2(4) + 1 = 9
f(4) = 9
This one fits here
This one fits here

6. Graph: For all x’s < 1, use the top graph (to the left of 1)
For all x’s ≥ 1, use the bottom graph (to the right of 1)

7. x = 1 is the breaking
point of the graph.
To the left is the top
equation.
To the right is the
bottom equation.

8. Point of Discontinuity
Graph:
Point of Discontinuity