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2.5 Piecewise- defined Functions
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Quiz Have you taken your Exam 1 yet?
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Piecewise-Defined Function
y 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
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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
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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)
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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
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Find The Formula For a Piecewise-defined Function
y Example: f(x) = -x if x ≤ 0 (1/3)x-1 if x > 0 x
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Homework PG. 132: 6-24(M3), 33, 36, 37, 52 KEY: 15, 36, 52 Reading: 2.6 Combinations
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