How do you find the asymptotes for # f(x)= (x+5)/(x+3)#?

1 Answer
Feb 20, 2016

Answer:

vertical asymptote at x = -3
horizontal asymptote at y = 1

Explanation:

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

solve x + 3 = 0 #rArr x = - 3 #

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

If the degree of the numerator and denominator are equal , the equation can be found by taking the ratio of leading coefficients. Here they are both degree 1.

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

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