Precalc - Rational Functions (Chapter 3)

n>m

n>m

no horizontal asymptote

n=m

HA: y=a/b

n<m

HA: y=0

zeroes of the denominator

vertical asymptote

zeroes of the numerator

x intercepts

function value at x=0

y intercept

common terms in factored numerator and denominator

there is a hole

x value of cancelled out term

x value of hole

plug cancelled x value back into function

y value of hole

degree of numerator is one more than the degree of denominator

there is a slant asymptote

numerator / denominator with long division

slope of slant asymptote