<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">\(y=\mathrm{f}(x)\)</th><th style="text-align: center; --cell-justify: center">Horizontal Transformation</th><th style="text-align: center; --cell-justify: center">Vertical Transformation</th></tr></thead><tbody><tr><td rowspan="2" style="text-align: center; --cell-justify: center">Translation</td><td style="text-align: center; --cell-justify: center">\(a\) units in the positive \(x\) direction:Replace \(x\) with \(x-a\)\(y=\mathrm{f}(x-a)\)</td><td style="text-align: center; --cell-justify: center">\(a\) units in the positive \(y\) direction:Replace \(y\) with \(y-a\)\(y-a=\mathrm{f}(x) \Leftrightarrow y=\mathrm{f}(x)+a\)</td></tr><tr><td style="text-align: center; --cell-justify: center">\(a\) units in the negative \(x\) direction: Replace \(x\) with \(x+a\) \(y=\mathrm{f}(x+a)\)</td><td style="text-align: center; --cell-justify: center">\(a\) units in the negative \(y\) direction:Replace \(y\) with \(y+a\)\(y+a=\mathrm{f}(x) \Leftrightarrow y=\mathrm{f}(x)-a\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Scaling</td><td style="text-align: center; --cell-justify: center">Scaling by a factor of \(a\) parallel to the \(x\)-axis:Replace \(x\) with \(\frac{x}{a}\)\(y=\mathrm{f}\left(\frac{x}{a}\right)\)</td><td style="text-align: center; --cell-justify: center">Scaling by a factor of \(a\) parallel to the \(y\)-axis:Replace \(y\) with \(\frac{y}{a}\)\(\frac{y}{a}=\mathrm{f}(x) \Leftrightarrow y=a\mathrm{f}(x)\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Reflection</td><td style="text-align: center; --cell-justify: center">Reflection about the \(y\)-axis:Replace \(x\) with \(-x\)\(y=\mathrm{f}(-x)\)</td><td style="text-align: center; --cell-justify: center">Reflection about the \(x\)-axis:Replace \(y\) with \(-y\) \(-y=\mathrm{f}(x) \Leftrightarrow y=-\mathrm{f}(x)\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Modulus</td><td style="text-align: center; --cell-justify: center">\(y=\mathrm{f}(|x|)\)Omit the negative \(x\) portion. (where \(x &lt; 0\))Retain the positive \(x\) portion of the graph and reflect it about the \(y\) axis.</td><td style="text-align: center; --cell-justify: center">\(y=|\mathrm{f}(x)|\)Reflect the negative \(y\) portion to positive about the \(x\) axis.Omit the negative \(y\) portion (where \(y &lt; 0\)).</td></tr></tbody></table></div></div>

Horizontal Transformation

Vertical Transformation

\(a\) units in the positive \(x\) direction:Replace \(x\) with \(x-a\)\(y=\mathrm{f}(x-a)\)

\(a\) units in the positive \(y\) direction:Replace \(y\) with \(y-a\)\(y-a=\mathrm{f}(x) \Leftrightarrow y=\mathrm{f}(x)+a\)

\(a\) units in the negative \(x\) direction: Replace \(x\) with \(x+a\) \(y=\mathrm{f}(x+a)\)

\(a\) units in the negative \(y\) direction:Replace \(y\) with \(y+a\)\(y+a=\mathrm{f}(x) \Leftrightarrow y=\mathrm{f}(x)-a\)

Scaling by a factor of \(a\) parallel to the \(x\)-axis:Replace \(x\) with \(\frac{x}{a}\)\(y=\mathrm{f}\left(\frac{x}{a}\right)\)

Scaling by a factor of \(a\) parallel to the \(y\)-axis:Replace \(y\) with \(\frac{y}{a}\)\(\frac{y}{a}=\mathrm{f}(x) \Leftrightarrow y=a\mathrm{f}(x)\)

Reflection about the \(y\)-axis:Replace \(x\) with \(-x\)\(y=\mathrm{f}(-x)\)

Reflection about the \(x\)-axis:Replace \(y\) with \(-y\) \(-y=\mathrm{f}(x) \Leftrightarrow y=-\mathrm{f}(x)\)

\(y=\mathrm{f}(|x|)\)Omit the negative \(x\) portion. (where \(x &lt; 0\))Retain the positive \(x\) portion of the graph and reflect it about the \(y\) axis.

\(y=|\mathrm{f}(x)|\)Reflect the negative \(y\) portion to positive about the \(x\) axis.Omit the negative \(y\) portion (where \(y &lt; 0\)).

Transformations of Graphs

H2 Math

International Baccalaureate Higher Level Mathematics

Transformations of Graphs

Question 13e67b90

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