## Technique 1

When $f(x)$ approaches towards $0$, $y=\dfrac{1}{f(x)}$ approaches towards $\infty$, the graph of $y=\dfrac{1}{f(x)}$ approaches the vertical asymptote(s).## Technique 2

The graph of $y=\dfrac{1}{f(x)}$ has vertical asymptotes at the $x$-intercepts of $y=f(x)$.## Technique 3

When $f(x)$ approaches towards $\infty$, $y=\dfrac{1}{f(x)}$ approaches towards $0$, the graph of $y=\dfrac{1}{f(x)}$ approaches the horizontal asymptote(s).## Technique 4

- When $f(x)=\pm1$, $\dfrac{1}{f(x)}=\pm1$. The graphs are in the same quadrant.
- When $f(x) \lt 0$, $\dfrac{1}{f(x)} \lt 0$.
- When $f(x) \gt 0$, $\dfrac{1}{f(x)} \gt 0$.

## Technique 5

- The minimum turning point of $f(x)$ gives the maximum turning point of the reciprocal function.
- The maximum turning point of $f(x)$ gives the minimum turning point of the reciprocal function.