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2.4 - 2.5 Families of Functions, Piecewise, and Transformations

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Piecewise functions consist of different function rules for different parts of the domain.

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2x + 1 if x 2 x 2 4 if x > 2 h(x) = h(1) = 2(1) + 1 = 1 h(4) = 4 2 4 = 12 Evaluate each piecewise function for x = 1 and x = 4. To evaluate any piecewise function for a specific input, find the interval of the domain that contains that input and then use the rule for that interval.

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2 x if x 1 5x if x > 1 g(x) = g(4) = 5(4) = 20 g(1) = 2 (1) = 1 2 Evaluate each piecewise function for x = 1 and x = 4.

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3x 2 + 1 if x < 0 5x 2 if x 0 g(x) = g(3) = 5(3) 2 = 13 g(1) = 3(1) 2 + 1 = 4 Evaluate each piecewise function for x = 1 and x = 3.

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g(x) = 1 4 Graph each function. x + 3 if x < 0 2x + 3 if x 0

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The rounding down function is also called the greatest integer function.

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Greatest integer or rounding down function

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Example: Describe the transformations that have taken place in each of the related graphs:

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