# 25 Piecewise- defined Functions

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```					2.5 Piecewise- defined Functions
Quiz
 Have you taken your Exam 1 yet?
Piecewise-Defined Function
y
 example                                 5
4

1

x
-2        1         5

f(x) = x2

f(x) = x2 if -2 ≤ x ≤ 1                x2 if -2 ≤ x ≤ 1
f(x) =
f(x) = x if 1 < x ≤ 5                  x if 1 < x ≤ 5
f(x) = x
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:

x if x ≥ 0
f(x) =
-x if x < 0
Graph a piecewise-defined Function

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

4      for x ≤ 0
f(x) =   - x2    for 0 < x ≤ 2
2x - 6 for x > 2
Find The Formula For a Piecewise-defined
Function
y
 Example:

-x2 +3    if x ≤ 0
f(x) =
(1/3)x-1 if x > 0

x
Homework
 PG. 132: 6-24(M3), 33, 36, 37, 52

 KEY: 15, 36, 52