Question

What are the vertical and horizontal asymptotes of f(x)=2x/x-1

Answer 1

Find the vertical and horizontal asymptotes of the graph of the function $f(x)=\dfrac{2x}{x-1}:$

1. Vertical asymptote.

Since the denominator of the fraction is $x-1,$ then the vertical asymptote is $x=1,$ because the domain of the function is $x\neq 1.$

2. Horizontal asymptote.

Rewrite the function f(x):

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

The horizontal asymptote has the equation $y=2.$

Answer: correct choice is B

Answer 2

Answer:

Answer is B

Step-by-step explanation: