<p>The graph of $y=\mathrm{f}\left( x \right)$ is given below. It has one vertical asymptote $x=-1$ and one oblique asymptote $y=x-4$. It cuts the $x$-axis at $x=0$ and $x=3$. It has turning points at $\left( -3,-9 \right)$ and $\left( 1,-1 \right)$.</p>
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<p>On separate diagrams, sketch the graphs of the following, stating the equations of any asymptotes, and indicating any axial intercepts and turning points.</p>
<ol class="abc-list"><li data-list-item-id="item-1760866927951-mynneafer" data-list-item-path="item-1760866927951-mynneafer"><div class="list-item-paragraph">$y=\frac{1}{\mathrm{f}\left( x \right)}$.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1760866929354-c1dtibox2" data-list-item-path="item-1760866929354-c1dtibox2"><div class="list-item-paragraph">$y=\mathrm{f}\,\mathrm{ }\!\!'\!\!\mathrm{ }\left( x \right)$.<span class="inline-marks">[3]</span></div></li></ol>

The graph of $y=\mathrm{f}\left( x \right)$ is given below. It has one vertical asymptote $x=-1$ and one oblique asymptote $y=x-4$. It cuts the $x$-axis at $x=0$ and $x=3$. It has turning points at $\left( -3,-9 \right)$ and $\left( 1,-1 \right)$.

On separate diagrams, sketch the graphs of the following, stating the equations of any asymptotes, and indicating any axial intercepts and turning points.

$y=\frac{1}{\mathrm{f}\left( x \right)}$.

$y=\mathrm{f}\,\mathrm{ }\!\!'\!\!\mathrm{ }\left( x \right)$.

Sketching Derivative Graphs

Applications of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

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