find the horizontal asymptote, if any, of the graph of the rational function. h(x) = (x^2 - 81)/(x + 9)…

find the horizontal asymptote, if any, of the graph of the rational function. h(x) = (x^2 - 81)/(x + 9) select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has two horizontal asymptotes. the top asymptote is , and the bottom asymptote is (type equations.) b. the function has one horizontal asymptote . (type an equation.) c. there are no horizontal asymptotes.

find the horizontal asymptote, if any, of the graph of the rational function. h(x) = (x^2 - 81)/(x + 9) select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has two horizontal asymptotes. the top asymptote is , and the bottom asymptote is (type equations.) b. the function has one horizontal asymptote . (type an equation.) c. there are no horizontal asymptotes.

Answer

Explanation:

Step1: Simplify the rational - function

First, factor the numerator $x^{2}-81=(x + 9)(x - 9)$. So, $h(x)=\frac{(x + 9)(x - 9)}{x + 9}=x - 9,x\neq - 9$. This is a linear function.

Step2: Analyze the degree of the function

The degree of a linear function $y=x - 9$ is 1. For a rational function $y=\frac{f(x)}{g(x)}$, if the degree of $f(x)$ is greater than the degree of $g(x)$ (here the degree of the simplified function $x-9$ is 1 and the degree of the denominator of the original non - simplified form after considering the cancellation is 0), there are no horizontal asymptotes.

Answer:

C. There are no horizontal asymptotes.