Chapter 11.4, Problem 66E

To determine

To graph: the function $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{\sqrt{{\mathrm{x}}^2+1}}$ . And how many horizontal asymptotes does the function appear to have and what are the horizontal asymptotes.

Answer to Problem 66E

Function appears to have two horizontal asymptotes, one at y = 1 as $\mathrm{x}\to \mathrm{\infty }$ , and one at y = -1 as $\mathrm{x}\to -\mathrm{\infty }$ .

Explanation of Solution

Given information: Given function is $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{\sqrt{{\mathrm{x}}^2+1}}$

Calculation:

The graph of the function is given below.

  

From the graph function appears to have two horizontal asymptotes, one at y = 1 as $\mathrm{x}\to \mathrm{\infty }$ , and one at y = -1 as $\mathrm{x}\to -\mathrm{\infty }$ .