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1.7 Piecewise Functions

Learn to identify and graph piecewise functions including step, greatest integer, and absolute value functions with this comprehensive guide. Understand how different equations apply for varying intervals of the domain.

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1.7 Piecewise Functions

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  1. 1.7 Piecewise Functions Objective: Identify and graph piecewise functions including greatest integer, step, and absolute value functions.

  2. Piecewise function: A function in which different equations are usedfor different intervals of the domain. Ex. 1) Graph 2 if x < -5 f(x) = x + 4 if -5<x<4 -½x if x>4

  3. Step function: A function whose graph is a series of disjoint lines or steps. A step function, written as f(x)=[x], where f(x) is the greatest integer NOT greater than x. “Floor Function” Greatest Integer Function: Ex.2) Graph f(x) = 3[x] What is the domain and range? http://www.youtube.com/watch?v=zl5QodAFuVk Absolute Value Function: A piecewise function written as f(x) = x where f(x) > 0 for all values of x. Looks like a V

  4. See example 3 in book Graph f(x) = - 2 x + 3 Ex. 4)

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