Chapter 3.7, Problem 21E

To determine

To find the vertical and horizontal asymptote of the rational function.

Answer to Problem 21E

The vertical asymptote is the line $x=2$ and the horizontal asymptote is the line $y=0$ , of the given rational function.

Explanation of Solution

Given information:

The rational function is $r\left(x\right)=\frac{5}{x-2}$

Calculation:

Vertical asymptote of $r\left(x\right)$ are the lines $x=a$ , where $a$ is the zero of the denominator.

Therefore,

The zero of the denominators is obtained as:

  $\begin{array}{l}x-2=0\\ x=2\end{array}$

Hence,

The vertical asymptote is the line $x=2$ .

Horizontal asymptote:

The degree of the numerator is 0 and denominator is 1.

Since, $n=0<m=1$ , so, horizontal asymptote of the rational function $r\left(x\right)$ is the line $y=0$ .

Hence,

The vertical asymptote is the line $x=2$ and the horizontal asymptote is the line $y=0$ , of the given rational function.