# How do you find the vertical, horizontal or slant asymptotes for (2x)/(x-1)?

Mar 8, 2016

vertical asymptote x = 1
horizontal asymptote y = 2

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero.To find the equation let the denominator equal zero.

solve: x - 1 = 0 → x = 1 is the asymptote.

Horizontal asymptotes occur as lim_(x→±∞) f(x) → 0

To find equation divide numerator/denominator by x

$\frac{2 x}{x - 1} = \frac{\frac{2 x}{x}}{\frac{x}{x} - \frac{1}{x}} = \frac{2}{1 - \frac{1}{x}}$

As x tends to ∞ , 1/x → 0 rArr y = 2/1 = 2 " is the asymptote "

Here is the graph of the function.
graph{2x/(x-1) [-10, 10, -5, 5]}