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1.6 Step and Piecewise Functions

1.6 Step and Piecewise Functions. Objective. To identify and graph step and piecewise-defined functions. Step Functions. Functions whose graphs resemble set of stairsteps are known as step functions. The most famous of the step functions is the greatest integer function.

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1.6 Step and Piecewise Functions

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  1. 1.6 Step and Piecewise Functions

  2. Objective • To identify and graph step and piecewise-defined functions.

  3. Step Functions • Functions whose graphs resemble set of stairsteps are known as step functions.

  4. The most famous of the step functions is the greatest integer function. • This function is denoted by

  5. Definition • The greatest integer function equals the greatest integer less than or equal to x.

  6. Example • A parking lot in downtown Houston charges $2.00 for the first hour and $1.00 for each additional hour. Graph the charges as a function of time. How much does it cost to park for 8 hours and 35 minutes.

  7. A function defined by two or more equations over a specified domain is called a piecewise function.

  8. Example 4 A Piecewise-Defined function • Graph the function

  9. Example 4 A Piecewise-Defined function • Evaluate the function when x = -1, 0 and 1

  10. Sketch the Graph of

  11. Sketch the Graph of

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