How do you find the asymptotes for y=3/(2x-1)y=32x1?

1 Answer
Nov 23, 2016

The vertical asymptote is x=1/2x=12
The horizontal asymptote is y=0y=0
No slant asymptote

Explanation:

The domain of yy is D_y=RR-{1/2}

As you cannot divide by 0, x!=1/2

So, x=1/2 is a vertical asymptote.

The degree of the numerator is < the degree of the denominator, so there is no slant asymptote.

lim_(x->-oo)y=lim_(x->-oo)3/(2x)=0^(-)

lim_(x->+oo)y=lim_(x->+oo)3/(2x)=0^(+)

So y=0 is a horizontal asymptote.

graph{(y-3/(2x-1))(y)=0 [-10, 10, -5, 5]}