Translations of Graphs
Translations of Graphs
For \(y=\mathrm{f}(x)\), a translation is implemented by replacing \(x\) for a horizontal movement or replacing \(y\) for a vertical movement.
Translation by \(a\) units in the positive \(y\)-direction
\(y=\mathrm{f}(x)\)
\(y-a=\mathrm{f}(x)\iff y=\mathrm{f}(x)+a\)
Translation by \(a\) units in the negative \(y\)-direction
\(y=\mathrm{f}(x)\)
\(y+a=\mathrm{f}(x)\iff y=\mathrm{f}(x)-a\)
Translation by \(a\) units in the positive \(x\)-direction
\(y=\mathrm{f}(x)\)
\(y=\mathrm{f}(x-a)\)
Translation by \(a\) units in the negative \(x\)-direction
\(y=\mathrm{f}(x)\)
\(y=\mathrm{f}(x+a)\)
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