Exercise 19 Page 512

We want to draw the asymptotes and the graph of the given function. We will start by considering some possible transformations.

Transformations of $f(x)=\frac{1}{x},x\ne 0$
Vertical Translations	$$\begin{array}{c}\text{Translation up }k\text{ units, }k>0\\ y=\frac{1}{x}+k\end{array}$$
	$$\begin{array}{c}\text{Translation down }k\text{ units, }k>0\\ y=\frac{1}{x}-k\end{array}$$
Vertical Stretch or Shrink	$$\begin{array}{c}\text{Vertical stretch, }a>1\\ y=\frac{a}{x}\end{array}$$
	$$\begin{array}{c}\text{Vertical shrink, }0<a<1\\ y=\frac{a}{x}\end{array}$$
Reflection	$$\begin{array}{c}\text{In the }x\text{-axis}\\ y=\frac{\text{-}1}{x}\end{array}$$

Note that if the graph of the function is translated, the asymptotes are also translated in the same distance and direction. Consider the function.