Reciprocal Functions
These techniques involves sketching the graph of $y=\dfrac{1}{f(x)}$ from the graph of $y=f(x)$.
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.
Example 1
Draw the reciprocal graph of the following function.
Example 2
Draw the reciprocal graph of the following function.
Example 3
Draw the reciprocal graph of the following function.
Example 4
Draw the reciprocal graph of the following function.
Example 5
Draw the reciprocal graph of the following function.
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