rational functions?

Question

hello. can you please explain how to graph rational functions. i'm really confused and i have equations like f(x)= x^3+1/x^2-4. and (x+2)(x-1)/(x-3)

Answer 1

The main ideas (assuming the function is in simplified form) are:

There are vertical asymptotes at the roots of the denominator.

There are zeros at the roots of the numerator.

You can easily see whether it's going to +infinity or -infinity as it approaches an asymptote by checking the sign of each factor of the numerator or denominator.