How do you find the vertical, horizontal and slant asymptotes of: #(3x-2) / (x+1)#?

1 Answer
Apr 27, 2016

Answer:

vertical asymptote x = -1
horizontal asymptote y = 3

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 + 1 = 0 → x = -1 , is the asymptote

Horizontal asymptotes occur as # lim_(x to +- oo) , f(x) to 0 #

divide terms on numerator/denominator by x

# ((3x)/x - 2/x)/(x/x + 1/x) = (3 - 2/x)/(1 + 1/x) #

as #x to +- oo , y to (3-0)/(1+0) #

#rArr y = 3 " 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{(3x-2)/(x+1) [-10, 10, -5, 5]}