Question

Which graph represents the function f(x)= 2x-1/x-1

Answer 1

The third answer is the right one. Or C

Answer 2

To determine which graph represents the function $f(x)=\dfrac{2x-1}{x-1}$ make following steps:

1. The vertical asymptote is $x=1.$

2. Simplify the function

$f(x)=\dfrac{2x-1}{x-1}=\dfrac{2x-1-1+1}{x-1}=\dfrac{2(x-1)+1}{x-1}=2+\dfrac{1}{x-1}.$

Then the horizontal asymptote is $y=2.$

Only option C contains graph with such asymptotes.

Answer: correct choice is C