Function Properties: Random Piecewise Function
- A B Cron
This study looks at a selected piecewise function and the effect called a stretch or a shrink. Many confuse a vertical stretch or shrink with the horizontal stretch or shrink. The base function is dotted and is for reference. By checking the On/Off box, you can view each horizontally or vertically stretch or shrink the piecewise function individually or both together. Definition: Given a function f(x) = If[x > -6 ∧ x < -4, x + 6, If[x > -4 ∧ x < -2, -(x) - 2, If[x > -2 ∧ x < 0, x + 2, If[x > 0 ∧ x < 2, -(x) + 2, If[x > 2 ∧ x < 4, x - 2, If[x > 4 ∧ x < 6, -(x) + 6]]]]]], a function p(x) = m f(x) is a vertical stretch if m > | 1 | and a vertical shrink if m < | 1 |. And a function q(x) = f(m x) is a horizontal shrink if m > | 1 | and a horizontal shrink if m > | 1 |. The slider n controls a value from -5 to 5, this changes the base function. The slider m controls the function multiplier to illustrate the stretch or shrink, you can click the play button in the lower left to animate this functions. The Modify Base box allows you to move sliders to translate f1 left-right or up-down of the base function displayed.
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade. TLW be able to differentiate between a vertical or horizontal stretch and shrink with piecewise functions. f1(x) = If[x > -6 ∧ x < -4, x + 6, If[x > -4 ∧ x < -2, -(x) - 2, If[x > -2 ∧ x < 0, x + 2, If[x > 0 ∧ x < 2, -(x) + 2, If[x > 2 ∧ x < 4, x - 2, If[x > 4 ∧ x < 6, -(x) + 6]]]]]] http://library.thinkquest.org/20991/alg2/quad2.html Stretching and Shrinking