Graph the rational functions . Include the graphs and equations of the asymptotes. 1.y=x2/(x-1) 2. y=(x2-1)/x

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.6: Rational Functions
Problem 98E
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Graph the rational functions . Include the graphs and equations of the asymptotes.

1.y=x2/(x-1)

2. y=(x2-1)/x

Expert Solution
Step 1

Given that the rational function,

Calculus homework question answer, step 1, image 1

To calculate the equation of asymptotic.

For a rational function, the vertical asymptotes are the undefined points or the zeros of the denominator of the function.

Calculus homework question answer, step 1, image 2

To calculate the horizontal asymptotes of  Calculus homework question answer, step 1, image 3

In horizontal asymptotes,

 

If degree of numerator=1+degree of denominator, then the asymptotes is a slant asymptotes of the form Calculus homework question answer, step 1, image 4

Degree of numerator=2 and degree of denominator=1

 

2=1+1

 

So the horizontal asymptotes is: Calculus homework question answer, step 1, image 5

 

The graph of the rational function is

Calculus homework question answer, step 1, image 6

 

 

 

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