<p class="paragraph-header">Horizontal Translation</p>
<p>Curve $C$ has equation $y=\mathrm{f}\left( x \right)$ where&nbsp;$\mathrm{f}\left( x \right)=\frac{1}{3}{{x}^{3}}-\frac{1}{3}{{x}^{2}}-3x+3$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The graph of ${y = \mathrm{f}(x - 2)}$</p><p>Replacing ${x}$ with ${x - 2}$</p><div class="graph-block" data-graph-config="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" data-width="200" data-height="200" style="width:200px;height:200px;max-width:100%;display:block;margin:0 auto;"></div><p>Graph of ${\mathrm{f}(x)}$ is translated ${2}$ units in the positive ${x}$ direction.</p></div><div class="question-column-divider"></div><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The graph of ${y = \mathrm{f}(x + 2)}$</p><p>Replacing ${x}$ with ${x + 2}$</p><div class="graph-block" data-graph-config="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" data-width="200" data-height="200" style="width:200px;height:200px;max-width:100%;display:block;margin:0 auto;"></div><p>Graph of ${\mathrm{f}(x)}$ is translated ${2}$ units in the negative ${x}$ direction.</p></div></div></div>
<p class="paragraph-header">Vertical Translation</p>
<p>Curve $C$ has equation $y=\mathrm{f}\left( x \right)$ where&nbsp;$\mathrm{f}\left( x \right)=\frac{1}{3}{{x}^{3}}-\frac{1}{3}{{x}^{2}}-3x+3$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The graph of ${y-2=\mathrm{f}(x) \Rightarrow y=\mathrm{f}(x)+2}$</p><p>Replacing ${y}$ with ${y-2}$</p><div class="graph-block" data-graph-config="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" data-width="200" data-height="200" style="width:200px;height:200px;max-width:100%;display:block;margin:0 auto;"></div><p>Graph of ${\mathrm{f}(x)}$ is translated 2 units in the positive ${y}$ direction.</p></div><div class="question-column-divider"></div><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The graph of ${y+2=\mathrm{f}(x) \Rightarrow y=\mathrm{f}(x)-2}$</p><p>Replacing ${y}$ with ${y+2}$</p><div class="graph-block" data-graph-config="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" data-width="200" data-height="200" style="width:200px;height:200px;max-width:100%;display:block;margin:0 auto;"></div><p>Graph of ${\mathrm{f}(x)}$ is translated 2 units in the negative ${y}$ direction.</p></div></div></div>

Curve $C$ has equation $y=\mathrm{f}\left( x \right)$ where $\mathrm{f}\left( x \right)=\frac{1}{3}{{x}^{3}}-\frac{1}{3}{{x}^{2}}-3x+3$.

Transformations of Graphs

H2 Math

International Baccalaureate Higher Level Mathematics

Transformations of Graphs

Question 6afa2a06

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