How do you find the asymptotes for f(x)= (2x+1)/(x-1)?

1 Answer
Feb 4, 2017

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

Explanation:

As you cannot divide by 0, x!=1

The vertical asymptote is x=1

As the degree of the numerator = the degree of the denominator,

there is no slant asymptote.

lim_(x->+-oo)f(x)=lim_(x->+-oo)(2x)/x=2

The horizontal asymptote is y=2

graph{(y-(2x+1)/(x-1))(y-2)(y-100x+100)=0 [-18.02, 18.03, -9.01, 9.01]}