Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 28

The graph of f is shown below.
Use it to sketch the graph of $\displaystyle y=\frac{1}{f(x)}$. In sketching $\displaystyle y=\frac{1}{f(x)}$, which features of $f$
are the most important? Explain how they are used.







$y=f(x)$ and $y = \displaystyle \frac{1}{f(x)}$ are exactly opposite in orientation, if the values
of $f(x)$ are large numbers, the values of $\displaystyle \frac{1}{f(x)}$ will be small. On the other hand, if the values of
$f(x)$ are small numbers the values of $\displaystyle \frac{1}{f(x)}$ will be large. As we refer to the graph of $f(x)$, we can obtain
the graph of $\displaystyle \frac{1}{f(x)}$ by simply making the orientation of $f(x)$ in a reverse manner as shown in the figure below.