To determine which graph represents the function [tex]f(x)=\dfrac{2x-1}{x-1}[/tex] make following steps:
1. The vertical asymptote is [tex]x=1.[/tex]
2. Simplify the function
[tex]f(x)=\dfrac{2x-1}{x-1}=\dfrac{2x-1-1+1}{x-1}=\dfrac{2(x-1)+1}{x-1}=2+\dfrac{1}{x-1}.[/tex]
Then the horizontal asymptote is [tex]y=2.[/tex]
Only option C contains graph with such asymptotes.
Answer: correct choice is C
