Modulus Transformations
Modulus Transformations
Vertical transformation: \(y=\lvert\mathrm{f}(x)\rvert\)
- Reflect the portion of \(y=\mathrm{f}(x)\) below the \(x\)-axis in the \(x\)-axis.
- Omit the original portion below the \(x\)-axis after reflecting it.
- Retain the portion of \(y=\mathrm{f}(x)\) on or above the \(x\)-axis.
\[\lvert\mathrm{f}(x)\rvert=\begin{cases}\mathrm{f}(x),&\mathrm{f}(x)\ge0,\\-\mathrm{f}(x),&\mathrm{f}(x)<0.\end{cases}\]
\(y=\mathrm{f}(x)\)
\(y=\lvert\mathrm{f}(x)\rvert\)
Horizontal transformation: \(y=\mathrm{f}(\lvert x\rvert)\)
- Omit the portion of \(y=\mathrm{f}(x)\) for \(x<0\).
- Reflect the retained portion for \(x\ge0\) in the \(y\)-axis.
- Retain the original portion for \(x\ge0\).
\[\mathrm{f}(\lvert x\rvert)=\begin{cases}\mathrm{f}(x),&x\ge0,\\\mathrm{f}(-x),&x<0.\end{cases}\]
\(y=\mathrm{f}(x)\)
\(y=\mathrm{f}(\lvert x\rvert)\)
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