Question

How do you find the vertical, horizontal and slant asymptotes of: `f(x)= (x)/(4x^2+7x+-2)`?

Answer 1

For + sign equation - Horizontal:`larr y = 0rarr`; and vertical : `uarr x =-1.39 and x = -0.34 darr`. For `-` sign- Horizontal: larr y=0rarr`; and vertical:`uarr x= -2 and x=1/4 darr#.

Explanation:

The zeros of the denominator `4x^2+7x+_2` are

`-1.39 and -0.34` for + sign `and -2 and 1/4` for - sign.

For the straight lines x = these values, `y to +-oo`.

Also, as #x to +-oo, y to 0.

graph{y(4x^2+7x+2)-x=0 [-20, 20, -10, 10]}
graph{y(4x^2+7x-2)-x=0 [-10, 10, -5, 5]}