Question

what are the vertical and horizontal asymptotes of $f(x)=\frac{2x}{x - 1}$?
horizontal asymptote at $y = 0$, vertical asymptote at $x = 1$
horizontal asymptote at $y = 2$, vertical asymptote at $x = 1$
horizontal asymptote at $y = 1$, vertical asymptote at $x = 0$
horizontal asymptote at $y = 1$, vertical asymptote at $x = 2$

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. For $f(x)=\frac{2x}{x - 1}$, $x-1=0$, so $x = 1$.

Step2: Find horizontal asymptote

Degree of numerator and denominator is 1. Divide leading - coefficients. Leading coefficient of numerator is 2 and of denominator is 1. So $y=\frac{2}{1}=2$.

Answer:

horizontal asymptote at $y = 2$, vertical asymptote at $x = 1$