Chapter 12.4, Problem 8E

To determine

To match: The function with its graph.

Answer to Problem 8E

The correct match of the given function with graph is $\left(\text{b}\right)$ .

Explanation of Solution

Given information:

The given function is,

  $f\left(x\right)=x-\frac{1}{x}$

Concept used:

The horizontal asymptote of the function is calculated as,

  $\begin{array}{l}\underset{x\to -\infty }{\lim }f\left(x\right)=L_1\\ \underset{x\to \infty }{\lim }f\left(x\right)=L_2\end{array}$

The given function is,

  $f\left(x\right)=x-\frac{1}{x}$

The horizontal asymptote of the function is calculated as,

  $\begin{array}{c}\underset{x\to \infty }{\lim }f\left(x\right)=\underset{x\to \infty }{\lim }\left(x-\frac{1}{x}\right)\\ =\infty -\frac{1}{\infty }\\ =\infty \end{array}$

The horizontal asymptote of the function is $\infty$ . So, the graph of the function match with $\left(\text{b}\right)$ .

Therefore, the correct match of the given function with graphis $\left(\text{b}\right)$ .