Question

Determine the vertical asymptote(s) of the given function. If none exists, state that fact. g(x)=x² +9x / x+11

A) x=−9,x=−11
B) x=−3,x=3
C) x=0,x=−3,x=3
D) x=0,x=−9

Answer 1

The function g(x) = (x² + 9x) / (x + 11) has a single vertical asymptote at x = -11, as this is the value that makes the denominator equal to zero and the function undefined.

Step-by-step explanation:

To determine the vertical asymptote(s) of the function g(x) = (x² + 9x) / (x + 11), we need to find where the function is undefined. This occurs when the denominator is zero, as dividing by zero is undefined in mathematics. Therefore, we set the denominator equal to zero and solve for x:

x + 11 = 0

x = -11

So, the vertical asymptote of the function g(x) is at x = -11. There are no other values for which the denominator equals zero, therefore, this is the only vertical asymptote. It's important to note that the numerator does not affect the location of vertical asymptotes, as they are determined solely by the values that make the denominator zero and therefore make the function undefined.