How do you find the vertical, horizontal or slant asymptotes for #(x-5)/(x+1)#?

1 Answer
Mar 15, 2016

Answer:

vertical asymptote x = - 1
horizontal asymptote y = 1

Explanation:

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

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

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

divide all terms on numerator / denominator by x

# (x-5)/(x+1) = (x/x -5/x)/(x/x + 1/x ) = (1 - 5/x)/(1 + 1/x) #

now as x → ∞ , # 5/x" and " 1/x → 0#

#rArr y = 1 " is the asymptote " #

Here is the graph of the function
graph{(x-5)/(x+1) [-20, 20, -10, 10]}