1. Evaluating Piecewise Functions

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

3. Evaluating Piecewise Functions
Steps:
Look at the domain to see which equation to use
Plug in x-value
Solve! 

4. f(x) = x2 + 1 , x  0 x – 1 , x  0 Let’s calculate f(-2).
You are being asked to output when x = -2. Since -2 is  0, you will only substitute into the first part of the function.
f(-2) = (-2)2 + 1 = 5

5. Evaluating Piecewise Functions
Which equation would we use to find; g(-5)? g(-2)? g(1)?

6. f(x) = 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1
Evaluate the following:
f(-2) = ? 2
f(3) =
-12 ?
f(-4) =
-14 ? ?
f(1) = -6

7. Graphically, the equation would look like this:
Step Functions
Looks like a flight of stairs
An example of a step function:
Graphically, the equation would look like this:

8. Step Functions
Evaluate:
f(0.5) =
f(1) =
f(2) =
f(3) =

9. Evaluate Piecewise
Evaluate:
f(-4) =
f(-2) =
f(1) =
f(3) =

10. Select Answers
3) f(-1) = -1 4) f(.5)= 3.75 f(0) = 0 f(1) = 3 f(4/3)= -4 f(3) = 6 f(4) = 7 7) f(.5) = 1 8) f(0) = 1 f(1) = 1 f(2) = 3 f(3)= 3 f(4)= 5 f(4)= 3 f(5)= 5 12) f(-4)= -4 13) f(1)= 3 f(-2)= -2 f(2)= 5 f(0)= 0 f(7)= 8 f(4)= --- f(11)= 5