Chapter 8.3, Problem 31PPSE

Solution

ToGraph:The rational function $y=\frac{x+4}{x-4}$ .

Given information:

The given rational function is $y=\frac{x+4}{x-4}$ .

Explanation:

Consider the given rational function.

Horizontal asymptotes:

The degree of the numerator is equal tothe denominator thus there is horizontal asymptotes is .

  $\begin{array}{l}y=\frac{1}{1}\\ y=1\end{array}$

Vertical asymptotes and Holes:

  $y=\frac{\left(x+4\right)}{\left(x-4\right)}$

There are no holes because the same factor does not exist in the numerator and denominator. Look at the denominator to find vertical asymptotes. There is a vertical asymptotes at $x=4$

  $x\text{and}y$ Intercept and other points

y-intercept $x=0$

  $y=\frac{0+4}{0-4}=-1$

The y − intercept is $\left(0,-1\right)$

x-intercept $y=0$

  $\begin{array}{c}0=\frac{x+4}{x-4}\\ x=-4\end{array}$

The y − intercept is $\left(-4,0\right)$

Some points especially around the asymptotes.

  $\begin{array}{cc}x& y\\ -10& .43\\ 3& -7\\ 5& 9\\ 8& 3\\ 15& 1.73\end{array}$

The required graph is shown below: