To calculate:The domain of rational function. Also, to find out the horizontal, vertical , or oblique asymptote.
Answer to Problem 32RE
The domain is
The vertical asymptote is
The horizontal asymptote is
Explanation of Solution
Given information:
The rational function
Formula used:
Vertical Asymptote: A rational function
asymptote
Horizontal Asymptote: If a rational function is proper , the line
Oblique Asymptote :it occur when the degree of the denominator of a rational
function is one less than the degree of the numerator. The asymptote will be along line
Calculation:
Consider ,
The domain of R is the set of all real numbers except
Now, Ris not in the lowest terms.
Numerator:-
Therefore,
Denominator:-
The line
Since the degree of the numerator ,1,is equal to the degree of denominator 1.The rational function is improper.
Using long division method we get,
As a result,
As
and
This implies
Hence, the domain of R is
The function has vertical and horizontal asymptote.
Vertical Asymptote at
Chapter 4 Solutions
Precalculus Enhanced with Graphing Utilities
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