Question

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

Answer 1

Horizontal asymptote: `larr y = 2 rarr`. x-intercept ( y = 0 ):`-5/3 and 8/3`. y-intercept ( x = 0 ): `-20`.

Explanation:

By actual division,

`y = 2-(3x+22)/(x^2+1)`

As `x to +-oo, 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]}