2.5 Piecewise- defined Functions

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Presentation transcript:

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 f(x) = x if 1 < x ≤ 5 f(x) = x2 if -2 ≤ x ≤ 1 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: f(x) = x if x ≥ 0 -x if x < 0

Graph a piecewise-defined Function Example: f(x) = x + 3 for -3 ≤ x < -1 Notice: When meeting with ‘<’ or ‘>’, use ‘ 。’ to mark the end point . Other cases, use ‘ . ’. 5 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)

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: 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