# How do you find the vertical, horizontal or slant asymptotes for #y=(x+3)/(x-3)#?

##### 1 Answer

May 3, 2016

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 set the denominator equal to zero.

solve : x - 3 = 0 → x = 3 is the asymptote

Horizontal asymptotes occur as

#lim_(x to +- oo), y to 0 # divide terms on numerator/denominator by x

#(x/x +3/x)/(x/x-3/x)=(1+3/x)/(1-3/x)# as

#x to +- oo , y to (1+0)/(1-0)#

# rArr y = 1 " is the asymptote "# Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here hence there are no slant asymptotes.

graph{(x+3)/(x-3) [-10, 10, -5, 5]}