Pre Calc Chapter 2 Section 6

Rational Functions Functions with the independent variable on the bottom of a fraction f(x) = N(x) D(x) Where N(x) & D(x) are polynomials and D(x) is not a zero Polynomial

Domain of a Rational Function The denominator can not = 0 As x approaches 0

x f(x) ∞ x f(x) ∞ From the Left From the Right

Range of a Rational Function As x approaches ∞

x ∞ f(x) From the Left From the Right x ∞ f(x)

What does that look like

Vertical Asymptotes f(x) = N(x) D(x) Where D(x) = 0 is a vertical asymptotes

Horizontal Asymptotes f(x) = N(x) D(x) If the degree of N(x) = n and the degree of D(x) = m If n<m the horizontal axis is the horizontal asymptote If n=m the line designated by y = the ratio of the leading coefficient N(x) over the leading coefficient of D(x) If n>m there is no horizontal asymptote