Chapter 5.4, Problem 12E

To determine

Graph each function. Show any asymptotes as dashed lines.

Answer to Problem 12E

Horizontal asymptote = $\mathrm{y}=10$

Explanation of Solution

Given :

The function is :

  $\mathrm{h}\left(\mathrm{x}\right)=\frac{10{\mathrm{x}}^2}{{\mathrm{x}}^2+1}$

Calculation:

Make a table of different values of function:

x	$\mathrm{h}\left(\mathrm{x}\right)=\frac{10{\mathrm{x}}^2}{{\mathrm{x}}^2+1}$
0	0
1	5
-1	5
$\mathrm{x}\to +\mathrm{\infty }$	$\mathrm{h}\left(\mathrm{x}\right)=\frac{10{\mathrm{x}}^2}{{\mathrm{x}}^2+1}\to 10$
$\mathrm{x}\to -\mathrm{\infty }$	$\mathrm{h}\left(\mathrm{x}\right)=\frac{10{\mathrm{x}}^2}{{\mathrm{x}}^2+1}\to 10$

Plot the points and we get the graph of the function.

  

An asymptote is a value of a function that you can get very near to, but you can never reach.

So, the function has one asymptote:

Horizontal asymptote = $\mathrm{y}=10$