How do you find the domain on a rational polynomial?

When finding the domain of rational polynomial (or any function) you want to find when the function doesn't exist, so in the case of a rational polynomial you want to find when the denominator is equal to 0, because we know 1/0 is an undefined number.

What does the sign of the first derivative mean for f(x)?

The sign of the first derivative tells whether f(x) is increasing, decreasing, or constant. If after you take the derivative of f(x) and the leading coefficient of f'(x) is positive, then it is increasing, if the leading coefficient is negative then f(x) is decreasing, and if f'(x) is a constant than f(x) is constant.

What real numbers are equal to their cubes?

Let the number be x. So, then set x=x^3 expanding x^3=x(x^2-1)=0 then we have x(x-1)(x+1)=0 Therefore our real numbers that are equal to their cubes are 0,1,-1