1. 2.5 Piecewise- defined Functions

2. Quiz
Have you taken your Exam 1 yet?

3. Piecewise-Defined Functiony
example 5 4 1 x -2 1 5
f(x) = x2
f(x) = x2 if -2 ≤ x ≤ 1
f(x) = x if 1 < x ≤ 5
f(x) =
x2 if -2 ≤ x ≤ 1
x if 1 < x ≤ 5
f(x) = x

4. Piecewise-defined Function
Definition: a Piecewise-defined Function is a function defined by different rules over different subsets of its domain
Typical example: f(x) = |x|
we can rewrite f(x) = |x| into piecewise-defined form as:
f(x) =
x if x ≥ 0
-x if x < 0

5. Graph a piecewise-defined Function
Example:
f(x) =
x for -3 ≤ x < -1
Notice: When meeting with ‘<’ or ‘>’, use ‘ 。’ to mark the end point . Other cases, use ‘ . ’.
for -1 ≤ x ≤ 1
√ x for 1 < x < 9
1, What is the domain?
2, What is the range?
3, Find f(0)
4, Find f(-5)
5, Find f(-1)

6. Graph of the Piecewise-defined Function
Sketch the graph of the piecewise defined function:
for x ≤ 0
f(x) =
- x for 0 < x ≤ 2
2x for x > 2

7. Find The Formula For a Piecewise-defined Functiony
Example:
f(x) =
-x if x ≤ 0
(1/3)x-1 if x > 0 x

8. Homework
PG. 132: 6-24(M3), 33, 36, 37, 52
KEY: 15, 36, 52
Reading: 2.6 Combinations