Question

How do you find the horizontal asymptote for `g(x)=(x+3)/(x(x+4))`?

Answer 1

`y=0`

Explanation:

`"horizontal asymptotes occur as"`

`lim_(xto+-oo)g(x)toc" (a constant)"`

`"divide terms on numerator/denominator by the highest"`
`"power of x, that is "x^2`

`g(x)=(x/x^2+3/x^2)/(x^2/x^2+(4x)/x^2)=(1/x+3/x^2)/(1+4/x)`

`"as "xto+-oo,g(x)to(0+0)/(1+0)`

`rArry=0" is the asymptote"`
graph{(x+3)/(x^2+4x) [-10, 10, -5, 5]}