2.5 Piecewise- defined Functions
Quiz

Have you taken your Exam 1 yet?
Piecewise-Defined Function

y
5
example
4
1
-2
1
5
x
f(x) = x2
f(x) = x2 if -2 ≤ x ≤ 1
f(x) = x if 1 < x ≤ 5
f(x) = x
f(x) =
x2 if -2 ≤ x ≤ 1
x if 1 < x ≤ 5
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
Graph a piecewise-defined Function

Example:
f(x) =
x+3
5
√x
1, What is the domain?
2, What is the range?
3, Find f(0)
4, Find f(-5)
5, Find f(-1)
for -3 ≤ x < -1
for -1 ≤ x ≤ 1
for 1 < x < 9
Notice: When
meeting with ‘<’ or
‘>’, use ‘ 。’ to
mark the end point .
Other cases, use ‘ . ’.
Graph of the Piecewise-defined Function

Sketch the graph of the piecewise defined function:
f(x) =
4
for x ≤ 0
- x2
for 0 < x ≤ 2
2x - 6 for x > 2
Find The Formula For a Piecewise-defined
Function

y
Example:
f(x) =
-x2 +3
if x ≤ 0
(1/3)x-1 if x > 0
x
Homework

PG. 132: 6-24(M3), 33, 36, 37, 52

KEY: 15, 36, 52

Reading: 2.6 Combinations