Chapter 11.4, Problem 7E

To determine

To Identify:

The function with its graph by using horizonal asymptotes as aids.

Answer to Problem 7E

The given function $4-\frac{1}{x^2}$ is match with the graph $\left(d\right)$ .

Explanation of Solution

Given Information:

  

  $f\left(x\right)=4-\frac{1}{x^2}$

Calculation:

The function is $f\left(x\right)=4-\frac{1}{x^2}$

To get the horizontal asymptote of the graph as follows,

  $\begin{array}{l}f\left(x\right)=4-\frac{1}{x^2}\\ f\left(x\right)=4\end{array}$

Where $x\to \infty$

Therefore, the horizontal asymptote of the graph will be $y=4$ .

Since the function has the vertical asymptote at $x=0$ .

Therefore, the only graph that has the horizontal asymptote as $y=4$ is the graph $\left(d\right)$ .

Hence, the graph that represents the function is $\left(d\right)$ .