Answer
The domain is $(-2,2)$
$f'(0) = -2$
$\lim\limits_{x \to 2^-}f(x) = \infty$
$f$ is discontinuous at $~~x = -1~~$ and $~~x = 1~~$
$f$ is odd
Work Step by Step
The domain is $(-2,2)$
$f'(0) = -2$
The slope at $~~x=0~~$ is $~~-2$
$\lim\limits_{x \to 2^-}f(x) = \infty$
As $x$ approaches $2$ from the left, the value of the function becomes larger magnitude positive numbers.
$f$ is discontinuous at $~~x = -1~~$ and $~~x = 1~~$
$f$ is odd
Then $f(-x) = -f(x)$ for all $x$ in $(-2,2)$
The graph is symmetric about the origin.
