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

1 Answer
Mar 8, 2016

Answer:

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

#(2x)/(x-1) = ((2x)/x)/(x/x- 1/x) = 2/(1 - 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]}