$\text { Describe the } x \text {-values at which the graph of the function } f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 9 } \text { given below }$
is differentiable.
A) $f ( x )$ is differentiable at $x = \pm 3$.
B) $f ( x )$ is differentiable everywhere except at $x = \pm 3$.
C) $f ( x )$ is differentiable everywhere except at $x = 0$.
D) $f ( x )$ is differentiable on the interval $( - 2,2 )$.
E) $f ( x )$ is differentiable on the interval $( 2 , \infty )$.

Question

$\text { Describe the } x \text {-values at which the graph of the function } f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 9 } \text { given below }$  
is differentiable.
A) $f ( x )$ is differentiable at $x = \pm 3$. 
B) $f ( x )$ is differentiable everywhere except at $x = \pm 3$. 
C) $f ( x )$ is differentiable everywhere except at $x = 0$. 
D) $f ( x )$ is differentiable on the interval $( - 2,2 )$. 
E) $f ( x )$ is differentiable on the interval $( 2 , \infty )$.

Quizplus · Accepted Answer

The function has vertical asymptotes at $x=-3$ and $x=3$, where the denominator becomes zero. At $x=0$, the function has a hole. Other than these three points, the function is continuous and differentiable, so the answer is (B).