Accurately graph the following function by determining the following: \( f(x)=\frac{x^{2}-16}{x^{2}-3 x-4} \)
a. Find the Vertical Asymptotes (Show all work):
b. Find the Horizontal Asymptote
c. Does the function have a hole? (Show all work)
d. Find the \( x \)-intercept.
e. Find the \( y \)-intercept.
f. Identify the domain and the range

Step 1 ：a. Vertical Asymptotes: \( x^{2} - 3x - 4 = (x - 4)(x + 1) \), so x = 4 or x = -1 are the vertical asymptotes.

Step 2 ：b. Horizontal Asymptote: Degree of numerator and denominator equal, so divide their leading terms: \( \frac{x^2}{x^2} \), so y = 1 is the horizontal asymptote.

Step 3 ：c. Hole: No holes, because no common factors in the numerator and denominator can be canceled.

Step 4 ：d. \( x \)-intercept: \( f(x) = 0 \Rightarrow x^2 - 16 = 0 \), thus x = ±4 are the \( x \) intercepts.

Step 5 ：e. \( y \)-intercept: f(0) = \( \frac{0^2 - 16}{0^2 - 3(0) - 4} \), thus y = 4 is the \( y \)-intercept.

Step 6 ：f. Domain: \( x \in \mathbb{R} \), except x = 4 and x = -1, Range: \( y \in \mathbb{R} \), except y = 1