$y=\mathrm{f}\left( x \right)$ $y=\frac{1}{\mathrm{f}\left( x \right)}$ \(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 $y=\dfrac1{f(x)}$: open limiting points $(-1,0)$, $(1,0)$, and maximum $(0,1)$. For $y=f'(x)$: vertical asymptotes $x=-1,1$, horizontal asymptote $y=0$, zero $(0,0)$, negative for $x0$, wherever defined.

Prelims Revision Set: Reciprocal and Gradient Graphs Q3

Prelims Revision Set: Reciprocal and Gradient Graphs Q3

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