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Question

Compare and discuss the long-run behaviors of the following functions:

$f(x)=\frac{x^2+1}{x^2+5}, \quad g(x)=\frac{x^3+1}{x^2+5}, \quad h(x)=\frac{x+1}{x^2+5} .$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 5Recall: The long-term behavior of a rational function

$y=r(x)=\frac{p(x)}{q(x)}$

where $p$ and $q$ are polynomials, equals the long-term behavior of

$y=\frac{\text{ Leading term of } p}{\text{ Leading term of } q}$

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