Find the vertical and horizontal asymptotes of the graph of the function [tex]f(x)=\dfrac{2x}{x-1}:[/tex]
1. Vertical asymptote.
Since the denominator of the fraction is [tex]x-1,[/tex] then the vertical asymptote is [tex]x=1,[/tex] because the domain of the function is [tex]x\neq 1.[/tex]
2. Horizontal asymptote.
Rewrite the function f(x):
[tex]f(x)=\dfrac{2x}{x-1}=\dfrac{2x-2+2}{x-1}=\dfrac{2(x-1)+2}{x-1}=2+\dfrac{2}{x-1}.[/tex]
The horizontal asymptote has the equation [tex]y=2.[/tex]
Answer: correct choice is B
