Question

How do you find vertical, horizontal and oblique asymptotes for `[(3x^2) + 14x + 4] / [x+2]`?

Answer 1

Vertical: `uarr x=-2 darr`
Oblique: `y=3x+8`, in both directions. See the graphs.

Explanation:

`(y(x+2)-3x^2) -14x-4=0`

Reorganizing to the form (ax+bx+c((a'x+b/y+c')=k,

`(x+2)(y-3x-8)=-12`

This represents a hyperbola with asymptotes

`(x+2)(y-3x-8)`=0

The first graph is asymptotes inclusive and the second is for the

hyperbola, sans asynptotes.

Note: The second degree equation

`ax^2+2hxy+by^2+...=0` represents a hyperbola, if `ab-h^2 < 0`. It

is so for the given equation.

graph{(y-3x-8)(x+2)((y-3x-8)(x+2)+14)=02 [-80, 80, -40, 40]}

graph{(y-3x-8)(x+2)+14=0 [-80, 80, -40, 40]}