Horizontal Scaling
Horizontal Scaling
In the following standard cases, \(a>1\). Replacing \(y\) controls a vertical scale; replacing \(x\) controls a horizontal scale.
Scale factor \(\dfrac{1}{a}\) parallel to the \(x\)-axis
\(y=\mathrm{f}(x)\)
\(y=\mathrm{f}(ax)\)
Scale factor \(a\) parallel to the \(x\)-axis
\(y=\mathrm{f}(x)\)
\(y=\mathrm{f}\left(\dfrac{x}{a}\right)\)
The diagrams illustrate \(\mathrm{f}(x)=\sin x\) with \(a=2\). All these functions have domain \(\mathbb R\); the markers identify selected corresponding zeros, and the curves continue beyond them. The transformed curve is blue; the dashed black curve is the original for comparison.
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