The diagram below shows the graph of $y=\mathrm{f}(x)$, where $y=3$ is a horizontal asympto

Question

The diagram below shows the graph of $y=\mathrm{f}(x)$, where $y=3$ is a horizontal asymptote. On separate diagrams, sketch the graph of $y=\mathrm{f}(2|x|)$.[3] the graph of $y=\dfrac{12}{\mathrm{f}(x)}$.[5] Your diagrams should include the coordinates of the points of intersection with the axes, the coordinates of any max or min points, the equations of any vertical and/or horizontal asymptotes.

Accepted Answer

(i) Intercepts $(\pm1,0)$, minimum $(0,-4)$, asymptote $y=3$. (ii) No x-intercept; maximum $(0,-3)$; asymptotes $x=\pm2$, $y=0$ on the left and $y=4$ on the right.

Solution:

Typed Solution