Question

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

Answer 1

`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]}