Chapter 9, Problem 4STP

To determine

To find: Which of the following is not an asymptotes of the rational function.

Answer to Problem 4STP

Correct option is (J).

Explanation of Solution

Given information:

The given rational function is $f\left(x\right)=\frac{1}{x^2-49}$ .

Calculation:

For the function $f\left(x\right)=\frac{1}{x^2-49}$ .

When x becomes larger and larger and approaches infinity then $f\left(x\right)$ approaches 0. Thus, $f\left(x\right)=0$ is an asymptote.

Also the function is not defined if denominator is zero. Therefore,

  $\begin{array}{l}{x}^2-49=0\\ \left(x-7\right)\left(x+7\right)=0\\ x-7=0\text{ or }x+7=0\\ x=7\text{ or }x=-7\end{array}$

Since, the function is not defined at $x=7$ and $x=-7$ then there are asymptotes at $x=7$ and $x=-7$ .

Therefore, there will be no asymptotes at $f\left(x\right)=1$

Hence,

Correct option is (J).