How do you find the end behavior of #f(x)= (3x+1)/x#?

1 Answer
Jan 11, 2016

Answer:

#lim_(x rarr -oo)(3x+1)/x=3#

#lim_(x rarr +oo)(3x+1)/x=3#

#:. y=3# horizontal asymptote

Explanation:

To find the end behavior of #f(x)# you have to evaluate:

#lim_(x rarr +-oo) f(x)#

  1. #lim_(x rarr -oo)(3x+1)/x~~lim_(x rarr -oo)(3x)/x=3#

  2. #lim_(x rarr +oo)(3x+1)/x~~lim_(x rarr +oo)(3x)/x=3#

Therefore

#y=3# is an horizontal asymptote

graph{(3x-1)/x [-8.72, 7.08, -1.28, 6.62]}