Chapter 11.4, Problem 5E

To determine

To Identify:

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

Answer to Problem 5E

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

Explanation of Solution

Given Information:

  

  $f\left(x\right)=\frac{4x^2}{x^2+1}$

Calculation:

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

To get the horizontal asymptote of the graph as follows,

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

Where $x\to \infty$

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

There are two graphs which has horizontal asymptote as $4$ . But in case of graph $\left(c\right)$ the graph passes through the origin which applicable for the given function hence the graph that represent the function is $\left(c\right)$ .