Provide an appropriate response.
-Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $$f ( x ) = \frac { - 4 } { ( x - 8 ) ^ { 2 } }$$
A) Approaches $- \infty$ from the left and the right
B) Approaches $\infty$ from the left, approaches $- \infty$ from the right
C) Approaches $\infty$ from the left and the right
D) Approaches $- \infty$ from the left, approaches $\infty$ from the right

Question

Quizplus · Accepted Answer

As $x$ approaches the vertical asymptote at $x = 8$, the denominator of the function $f(x) = \frac{-4}{(x - 8)^2}$ approaches 0, making the value of the function increasingly negative, regardless of the direction from which $x$ approaches 8. Since the square of any real number is positive, and the numerator is negative, the function approaches $-\infty$ from both the left and the right.

Provide an Appropriate Response f(x)=−4(x−8)2f ( x ) = \frac { - 4 } { ( x - 8 ) ^ { 2 } }f(x)=(x−8)2−4​

Provide an Appropriate Response $f ( x ) = \frac { - 4 } { ( x - 8 ) ^ { 2 } }$