Consider the rational function defined by $f(x)=\frac{x^{2}+3 x-4}{x^{2}-x-2}$. 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 $f$.

Question

Quizplus · Accepted Answer

The Answer is (a)

x=-1 ; x=2

(b)

y=1

(c) 2
(d)

-4 ; 1

(e)

\left(\frac{1}{2}, 1\right)

$(a) x=-1 ; x=2 (b) y=1 (c) 2 (d) -4 ; 1 (e) \left(\frac{1}{2}, 1\right)$

Consider the Rational Function Defined By f(x)=x2+3x−4x2−x−2f(x)=\frac{x^{2}+3 x-4}{x^{2}-x-2}f(x)=x2−x−2x2+3x−4​ Determine the Answers to (A) - (E) Analytically: (A)

Consider the Rational Function Defined By $f(x)=\frac{x^{2}+3 x-4}{x^{2}-x-2}$ Determine the Answers to (A) - (E) Analytically:
(A)