How do you graph y=(2x^2-3x-20)/(x^2+1) using asymptotes, intercepts, end behavior?

Dec 23, 2016

Answer:

Horizontal asymptote: $\leftarrow y = 2 \rightarrow$. x-intercept ( y = 0 ):$- \frac{5}{3} \mathmr{and} \frac{8}{3}$. y-intercept ( x = 0 ): $- 20$.

Explanation:

By actual division,

$y = 2 - \frac{3 x + 22}{{x}^{2} + 1}$

As $x \to \pm \infty , y \to 2$.

y'=0, at x = 0.68 ( near the y-axis ) and -14.7 ( nearer to the asymptote y = 2 ), nearly

graph{(y-2)(x^2+1)+3x+22=0 [-15.81, 15.82, -50, 3.94]}