Find the asymptotes of the function
Answer to Problem 36CR
Vertical asymptote: x = − 2 and Horizontal Asymptote y = 0
Explanation of Solution
Given:
Find the asymptotes of the function
Concept Used:
To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x. We must set the denominator equal to 0 and solve.
The vertical asymptotes will occur at those values of x for which the denominator is equal to zero.
To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote
Calculation:
Calculation:
The vertical asymptotes will occur at those values of x for which the denominator is equal to zero.
Vertical asymptote:
To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
Horizontal Asymptote y = 0
Vertical asymptote:
The graph of the function:
Thus, Vertical asymptote: x = − 2 and Horizontal Asymptote y = 0
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