Question

How do you find the horizontal asymptote for `y = x / (x-3)`?

Answer 1

`"horizontal asymptote at "y=1`

Explanation:

`"Horizontal asymptotes occur as"`

`lim_(xto+-oo),yto c" (a constant)"`

`"divide terms on numerator/denominator by "x`

`y=(x/x)/(x/x-3/x)=1/(1-3/x)`

`"As "xto+-oo,yto1/(1-0)`

`y=1" is the asymptote"`
graph{x/(x-3) [-10, 10, -5, 5]}