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Special Functions Objective: Write and graph piecewise and absolute value functions.

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Piecewise Functions A truck driver earns $21.00 per hour for the first 40 hours worked in one week. The driver earns time- and-a-half, or $31.50, for each hour worked in excess of 40. The pair of function rules below represent the drivers wage, w(h), as a function of the hours worked in one week, h.

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Example 1

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Try This Graph:

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Try This Graph: -2x + 1 x y -2 5 1 -1

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Try This Graph:

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Try This Graph: x – 4 x y 1 -3 5 1

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Try This Graph:

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Try This

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Writing Equations Write the piecewise function represented by the graph below.

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Writing Equations Write the piecewise function represented by the graph below.

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Writing Equations Write the piecewise function represented by the graph below.

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Writing Equations Write the piecewise function represented by the graph below.

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Absolute Value The absolute value function, denoted by f(x) = |x|, can be defined as a piecewise function as follows:

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Absolute Value The absolute value function, denoted by f(x) = |x|, can be defined as a piecewise function as follows:

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Example 4

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Homework Page 129 17-27 odd 58, 59

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1 What you will learn today 1. How to evaluate piecewise functions 2. How to graph piecewise functions 3. How to determine piecewise functions from a graph.

1 What you will learn today 1. How to evaluate piecewise functions 2. How to graph piecewise functions 3. How to determine piecewise functions from a graph.

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