-intercepts are the points where each is a real zero of the numerator function. The -intercept is the point where and is the numerator function. There is a vertical asymptote at the line for each factor of the denominator function that is not also a factor of the numerator function. There is a hole where ever a linear factor of the denominator has a common linear factor in the numerator.
Horizontal asymptotes:
Case 1: The degree of the numerator polynomial is smaller than the degree of the denominator polynomial -- the line (i.e. the -axis) is the horizontal asymptote.
Case 2: The degree of the numerator polynomial is equal to the degree of the denominator polynomial -- the line where is the lead coefficient of the numerator polynomial and is the lead coefficient of the denominator polynomial.
Case 3: The degree of numerator polynomial is greater than the degree of the denominator polynomial -- there is no horizontal asymptote, rather there is a slant asymptote. The RHS of the equation of the slant asymptote is the quotient obtained from performing polynomial long division excluding any remainder.
John
My calculator said it, I believe it, that settles it
