Vertical Stretching and Compression(scaling) of Graphs

This applet helps you explore, interactively, and understand the stretching and compression of the graph of a function when this function is multiplied by a constant a.

The function to be analyzed is of the form a*f(x). In this tutorial you may use f(x) = ||x|-2| (a "W" shaped graph), f(x) = x2 or f(x) = x3.


How does the multiplication of a function by a positive constant affect the graph of this function ?

1-Use the scrollbar to set the constant a to different values and observe the effect on the graph.

What is the range of values of the constant that create a vertical compression?

What is the range of values of the constant that create a vertical stretching?

What values reflect the graph on the x axis?

Explain analytically.

You have the choice (left panel, top) of any of the three functions
f(x) = ||x|-2| (this has a "W" shaped graph), f(x) = x
2 or f(x) = x3.

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Updated: February 2015

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