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Special Functions

Special Functions. Step Constant Identity Absolute Value Piece Wise. Step Function or Greatest Integer Function written [[x]] in the book. The step function looks like stairs!. The symbol [[x]] means. the greatest integer less than or equal to x. Therefore, [[7.5]]= 7

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Special Functions

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  1. Special Functions Step Constant Identity Absolute Value Piece Wise

  2. Step Functionor Greatest Integer Functionwritten [[x]] in the book The step function looks like stairs!

  3. The symbol [[x]] means • the greatest integer less than or equal to x. • Therefore, [[7.5]]= 7 [[-1.5]]= -2 because -1 > -1.5 [[1.5]]= 1

  4. The most common real life example is postage. A one ounce letter costs 34 cents. If it weights 1.5 ounces it still costs 34 cents! The cost changes with each ounce. Thus forming the steps.

  5. Each step has a closed circle on one side of the step and an open circle on the other. What does the closed circle represent? What does the open circle represent? Example 1 p.89 and 90.

  6. The Constant Function The constant function is a horizontal line. The equation for a horizontal line is? y= any number It has no slope or zero slope!

  7. The Identity Function The identity function is y=x, where the slope is 1 and the y-intercept is 0.

  8. Absolute Value Function Recall that the absolute value of a positive or a negative number is always positive. Whether we substitute -1 or 1 for x we will still have y=1. This is true for all real numbers substituted for x.

  9. The Absolute Value Function • Example p.91 in the book • Absolute Value Dynamic Worksheet The absolute value function can be written as: f(x) = {-x if x < 0, x if x > 0} A function using two or more expressions is called a piecewise function.

  10. Piecewise Function A piecewise function is a combination of more than one function graphed according to limits placed on each function. http://www.math.uky.edu/~pkoester/teaching/Fall_2009/Math123/GeoGebra/Continuous1.html

  11. Piecewise Function • Example p.92 • Piecewise Applet • Piecewise Functions

  12. Graphing Special Functions • When graphing these functions by hand it is easiest to create a table of values. • Then recall the qualities of the function to complete the graph. • Do the problems on page 94 #24, 26, 30, 32, 34, 38, and 40. Then work on the worksheets.

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