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Chapter 2: Problem 118

If you are given the equation of a rational function, how can you tell if the graph has a slant asymptote? If it does, how do you find its equation?

Short Answer

Expert verified
To determine if a graph of a rational function has a slant asymptote, the degree of the numerator must be exactly one more than the degree of the denominator. If it does meet this condition, perform polynomial long division to find the equation of the slant asymptote.

Step by step solution

01

Identify the degree of each polynomial

Look at the rational function given and identify the degree (the highest power of x) for the numerator and the denominator.
02

Check if the rational function has a slant asymptote

If the degree of the numerator is exactly one more than the degree of the denominator, it indicates that the graph of the rational function has a slant or oblique asymptote.
03

Find the equation of the slant asymptote

If the rational function does have a slant asymptote, use polynomial long division to divide the numerator by the denominator. The quotient (excluding the remainder), represented as a linear equation \(y = mx + b\), is the equation of the slant asymptote.

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