Stretching and Compressing a Graph — Cheat sheet

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Key method

For $g(x)=a f(bx)$ with nonzero $a,b$ , $(u,v)$ becomes $(u/b,av)$ . Thus $|a|>1$ stretches vertically, while $|b|>1$ compresses horizontally. Negative factors also reflect.

Example

For $f(x)=x^2$ , $g(x)=3f(x)$ triples every output. The point $(2,4)$ becomes $(2,12)$ . For $h(x)=f(2x)$ , the same old input $2$ is reached at $x=1$ , so its point becomes $(1,4)$ . Although $f(2x)=4x^2$ here, horizontal and vertical scaling are different constructions.

Avoid this mistake

A multiplier of zero collapses a graph and is not an invertible stretch. Track this as its own case.