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

Question

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

Accepted Answer

For $y=\dfrac1{f(x)}$: vertical asymptote $x=-1$, horizontal asymptote $y=\dfrac12$, open limiting point $(-2,0)$, points $\left(0,\dfrac13\right)$ and $\left(3,\dfrac15\right)$, with the latter a minimum. For $y=f'(x)$: vertical asymptote $x=-2$, horizontal asymptote $y=0$, zero $(3,0)$, positive for $x3$.

Prelims Revision Set: Reciprocal and Gradient Graphs Q7

Prelims Revision Set: Reciprocal and Gradient Graphs Q7

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