Question

 use a graphing utility to graph and  in the same viewing window to verify that the two functions are equal. Explain why they are equal. Identify any asymptotes of the graphs.

Answer 1

Step 1:

The functions are and  .

Let 

From Pythagorean theorem,

Step 2:

Substitute

The functions are equal.

Step 3:

Find the asymptotes of  .

Find the vertical asymptotes by solving zeros of denominator.

Since the roots are imaginary,  there is no vertical asymptotes.

 

To find horizontal asymptote, first find the degree of the numerator and  the degree of denominator.

Degree of the numerator = 1 and the degree of denominator = 1.

Since the degree of the numerator is equal to the degree of the denominator,horizontal asymptote is the ratio of the leading coefficient of numerator and denominator.

Horizontal asymptotes are at  .

Graph :

.