Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 2 } { ( x - 3 ) ^ { 2 } }$
A) Approaches $\infty$ from the left, approaches $- \infty$ from the right
B) Approaches $\infty$ from the left and 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

The graph of $f(x) = \frac{2}{(x - 3)^2}$ has a vertical asymptote at $x = 3$. As $x$ approaches 3 from either the left or the right, the denominator approaches 0, making the value of $f(x)$ approach $\infty$. The square in the denominator ensures the result is positive regardless of the direction from which $x$ approaches 3.

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