1. Pre Calc Chapter 2 Section 6

2. 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

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

4. x-.5-.1-.0001-.0000001 0 f(x)-2-10-10000-10000000 - ∞ x1.5.1.0001.0000001 0 f(x)12101000010000000 ∞ From the Left From the Right

5. Range of a Rational Function As x approaches ∞

6. x11010010001000000 ∞ f(x)11.01.001.000001 0 From the Left From the Right x-10-100-1000-1000000 - ∞ f(x)-.1-.01-.001-.000001 0

7. What does that look like

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

10. 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