Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { ( x - 2 ) ^ { 2 } }$
A) Approaches $- \infty$ from the left and the right
B) Approaches $\infty$ from the left and the right
C) Approaches $\infty$ from the left, approaches $- \infty$ from the right
D) Approaches $- \infty$ from the left, approaches $\infty$ from the right

Question

Quizplus · Accepted Answer

As $x$ approaches the vertical asymptote at $x = 2$, the denominator $(x - 2)^2$ approaches $0$, but since it is squared, it remains positive, making the overall fraction negative. Therefore, the graph approaches $-\infty$ from both the left and the right of $x = 2$.

Provide an Appropriate Response f(x)f ( x )f(x) As It Approaches Its Vertical Asymptote

Provide an Appropriate Response $f ( x )$ As It Approaches Its Vertical Asymptote