This study looks at basic function families 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 stretch or shrink individually or together.
Definition: Given a function f(x),
a function 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 integer slider power controls a value from -5 to 5, this changes the power of 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 Change Function box allows you to move sliders to vary the 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 various basic functions.
http://www.cattail.nu/school_web/math107/squish/index.html