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 to 0: $x-1=0$
Solve for $x$: $x=1$

Step2: Find horizontal asymptote

Compare degrees of numerator/denominator. Both degree 1.
Take ratio of leading coefficients: $\frac{2}{1}=2$, so $y=2$

Answer:

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