How do you find all the asymptotes for #f(x) = (3x^2 + 2x - 5)/(x - 4)#?

1 Answer
Nov 28, 2017

V.A. #x=4#
H.A. non
S.A. #3x+14#

Explanation:

. For a function to have vertical asymptote, the function needs to have undefined points also known as zeros of denominator.
#x-4#
#x=4# #<-# vertical asymptote

. When the degree of denominator is greater than the degree of the numerator the function will have a horizontal asymptote.
in this function degree of numerator is 2 and the degree of denominator is 1
#2>1# there fore this function does not have a horizontal asymptote

. to find slant asymptote, use polynomial long division
enter image source here

Slant Asymptote is #3x+14#