1. Section 9-1 Graphing Rational Functions

2. Def: A rational function is of the form Where p(x) and q(x) are rational polynomials and The line that the graph of a rational function approaches is called the _________?________ The line that the graph of a rational function approaches is called the _________?________

3. 1.) Graph: Note: x cannot equal ___?____ because it would be undefined Note: x cannot equal ___?____ because it would be undefined

4. There are three types of asymptotes 1.Vertical 2.Horizontal 3.Oblique or Slant

5. To find horizontal asymptotes: 1.If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). 2.If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote. 3.If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

6. One way to remember this is the following the pnemonic device: BOBO BOTN EATS DC BOBO BOTN EATS DC BOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none EATS DC - Exponents are the same, divide coefficients l BOBO BOTN EATS DC BOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none EATS DC - Exponents are the same, divide coefficients l

7. 2.) Graph: Find the domain and range

8. 3.) Graph:

9. 4.) Graph:

10. 5.) Graph: Find the discontinuity

11. Homework Practice 9-1 and Page 553 Problems: 1,5,14,15 and 25 Plot your graphs on graph paper Make sure to label your grid