1. 2.5 Piecewise Functions

2. Up to now, we’ve been looking at functions represented by a single equation.
In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain.
These are called piecewise functions.

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

4. Evaluate f(x) when x=0, x=2, x=4
First you have to figure out which equation to use
You NEVER use both
X=4
X=2
X=0
This one fits
Into the top
equation
So:
0+2=2
f(0)=2
So:
2(4) + 1 = 9
f(4) = 9
This one fits here
So:
2(2) + 1 = 5
f(2) = 5
This one fits here

5. 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)

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

7. Graph: Point of Discontinuity
Just like the step function, we must use open and closed circles so the graph will pass the vertical line test.

8. Graph First graph the absolute value on the left
Then, graph the quadratic on the right.