find any horizontal or vertical asymptotes. f(x) = (x² - 100)/(x + 10) select the correct choice below and…

find any horizontal or vertical asymptotes. f(x) = (x² - 100)/(x + 10) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the equation(s) of the vertical asymptote(s) is/are x = (type an exact answer using radicals as needed. use a comma to separate answers as needed.) b. there is no vertical asymptote. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the equation(s) of the horizontal asymptote(s) is/are y = (type an exact answer using radicals as needed. use a comma to separate answers as needed.) b. there is no horizontal asymptote.

find any horizontal or vertical asymptotes. f(x) = (x² - 100)/(x + 10) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the equation(s) of the vertical asymptote(s) is/are x = (type an exact answer using radicals as needed. use a comma to separate answers as needed.) b. there is no vertical asymptote. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the equation(s) of the horizontal asymptote(s) is/are y = (type an exact answer using radicals as needed. use a comma to separate answers as needed.) b. there is no horizontal asymptote.

Answer

Explanation:

Step1: Simplify the function

First, factor the numerator $x^{2}-100=(x + 10)(x - 10)$. So $f(x)=\frac{(x + 10)(x - 10)}{x+10}=x - 10,x\neq - 10$.

Step2: Find vertical asymptotes

A vertical asymptote occurs where the denominator of a rational - function is zero and the numerator is non - zero. Since $f(x)$ simplifies to a linear function after canceling out the common factor $(x + 10)$ in the numerator and denominator, there is no value of $x$ that makes the denominator zero while the numerator is non - zero. So there is no vertical asymptote.

Step3: Find horizontal asymptotes

The function $f(x)=x - 10$ is a linear function. For a non - constant linear function $y=mx + b$ ($m\neq0$), as $x\to\pm\infty$, $y$ also goes to $\pm\infty$. So there is no horizontal asymptote.

Answer:

B. There is no vertical asymptote. B. There is no horizontal asymptote.