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 [color=#c51414]dotted[/color] and is for reference.[br][br]By checking the [color=#c51414]On/Off box[/color], you can view each horizontally or vertically stretch or shrink the piecewise function individually or both together.[br][br]Definition: Given a function [b]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]]]]]][/b],[br]a function p(x) = m f(x) is a vertical stretch if m > | 1 | and a vertical shrink if m < | 1 |.[br]And a function q(x) = f(m x) is a horizontal shrink if m > | 1 | and a horizontal shrink if m > | 1 |.[br][br]The slider n controls a value from -5 to 5, this changes the base function.[br][br]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.[br][br]The Modify Base box allows you to move sliders to translate f1 left-right or up-down of the base function displayed.