Rational function properties
Domain (values of x that don't make the denominator zero)
intercepts (set y = 0 and solve for x)
intercept (set x = 0)
Zeros (same as x-intercepts)
Vertical asymptotes (values of x that make the denominator zero)
Horizontal asymptotes (y = a/b if degree of numerator < degree of denominator, y = none if degree of numerator > degree of denominator)
Holes (removable discontinuities where the numerator and denominator have common factors)