Consider the Rational Function Defined By $f(x)=\frac{x^{2}-2 x-3}{x^{2}+2 x-8}$ Determine the Answers to (A) - (E) Analytically:
(A)

Essay

Consider the rational function defined by $f(x)=\frac{x^{2}-2 x-3}{x^{2}+2 x-8}$ . Determine the answers to (a) - (e) analytically:
(a) Equations of the vertical asymptotes
(b) Equation of the horizontal asymptote
(c) $y$ -intercept
(d) $x$ -intercepts, if any
(e) Coordinates of the point where the graph of $f$ intersects its horizontal asymptote. Now sketch a comprehensive graph of $f$ .