How do you find the Vertical, Horizontal, and Oblique Asymptote given y=(3x+1)/(2-x)?

1 Answer
Feb 3, 2017

The vertical asymptote is x=2
The horizontal asymptote is y=-3
No oblique asymptote

Explanation:

As you cannot divide by 0, x!=2

The vertical asymptote is x=2

As the degree of the numerator is = to the degree of the denominator, there is nooblique asymptote.

lim_(x->+-oo)y=lim_(x->+-oo)(3x)/-x=-3

Therefore,

the horizontal asymptote is y=-3

graph{(y-(3x+1)/(2-x))(y+3)(y+50x-100)=0 [-20.62, 19.94, -10.68, 9.6]}