Question

How do you find the asymptotes for `f(x) = (3 - x) / x^2`?

Answer 1

The vertical asymptote is `x=0`
The horizontal asymptote is `y=0`

Explanation:

As you cannot divide by 0, the vertical asymptote is `x=0`

There is no slant asymptote as the degree of the numerator is less than the degree of the denominator:

`lim_(n rarr -oo )(3-x)/x^2=lim_(n rarr -oo )-x/x^2=lim_(n rarr -oo )-1/x=0^+`

`lim_(n rarr +oo )(3-x)/x^2=lim_(n rarr +oo )-x/x^2=lim_(n rarr +oo )-1/x=0^-`

The horizontal asymptote is `y=0`
graph{(3-x)/x^2 [-10, 10, -5, 5]}