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2.5 Piecewise- defined Functions

2.5 Piecewise- defined Functions. Quiz. Have you taken your Exam 1 yet?. Piecewise-Defined Function. example. y. 5. 4. 1. x. 1. 5. -2. f (x) = x 2. f (x) = x 2 if -2 ≤ x ≤ 1 f (x) = x if 1 < x ≤ 5 . f(x) = . x 2 if -2 ≤ x ≤ 1. x if 1 < x ≤ 5. f (x) = x.

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2.5 Piecewise- defined Functions

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  1. 2.5 Piecewise- defined Functions

  2. Quiz • Have you taken your Exam 1 yet?

  3. Piecewise-Defined Function • example y 5 4 1 x 1 5 -2 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 + 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)

  6. 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

  7. Find The Formula For a Piecewise-defined Function • Example: y x f(x) = -x2 +3 if x ≤ 0 (1/3)x-1 if x > 0

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

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