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

1 Answer
Nov 7, 2016

Answer:

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]}