Given $f(x) = \frac{6x^2 + 18x + 12}{-2x^2 + 6x + 8}$, which can be written in factored form as $f(x) = \frac{6(x+1)(x+2)}{-2(x+1)(x-4)}$, answer the following questions.
a. Provide the location of any removable discontinuities. [If there are none, enter \"DNE\".]
$x = -1$
b. Determine the value of the vertical intercept.
$y = (0, \frac{3}{2})$
c. List all of the horizontal intercepts. [If there is more than one, enter your answer as a comma-separated list.]
$x = -1, -2$
d. What is the function's end behavior?
As $x \to \pm \infty$, $f(x) \to -3$
e. Provide the locations of any vertical asymptotes. [If there is more than one, enter your answer as a comma-separated list. If there are none, enter \"DNE\".]
$x = -1, 4$
