How do you find vertical, horizontal and oblique asymptotes for #f(x)= (x+5)/(x+3)#?

1 Answer
Mar 30, 2016

Answer:

vertical asymptote x = - 3
horizontal asymptote y = 1

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 + 3 = 0 → x = -3 is the asymptote

Horizontal asymptotes occur as #lim_(xtooo) f(x) to 0#

divide terms on numerator/denominator by x

#rArr (x/x + 5/x)/(x/x + 3/x) = (1 + 5/x)/(1 + 3/x) #

As x#tooo , 5/x" and " 3/x to 0 #

#rArr y = 1/1 = 1 " is the asymptote " #

Here is the graph of f(x).
graph{(x+5)/(x+3) [-10, 10, -5, 5]}