1. Rational Functions

2. 5 values to consider 1)Domain 2)Horizontal Asymptotes 3)Vertical Asymptotes 4)Holes 5)Zeros

3. Domain In general, the domain of a rational function includes all real numbers except those x-values that make the denominator zero

4. Examples Find the domain of each:

5. Horizontal Asymptote Describes the end behavior of the graph as x approaches If the degree of p(x) < the degree of q(x), there is a horizontal asymptote at y = 0 If the degree of p(x) > the degree of q(x), there is NO horizontal asymptote If the degree of p(x) = the degree of q(x), there is a horizontal asymptote at

6. Holes in the graph Do not occur unless there are factors in p(x) that are the same as factors in q(x) Occur at the places where the numerator and denominator have the same solution (Cancels out of top and bottom)

7. Vertical Asymptote Shows excluded values for which the function, f(x) is not defined for x The graph of f has vertical asymptotes at the solutions to the denominator

8. Zeros The x-intercepts Occur when the numerator is equal to zero.

9. Ex1) Give the domain, asymptotes, holes and zeros. Then graph the function.

10. Ex2) Find the domain, asymptotes, holes and zeros. Then graph the function.

11. Ex3) Find the domain, asymptotes, holes and zeros. Then graph the function.

12. Ex4) Find the domain, asymptotes, holes and zeros. Then graph the function.

13. Practice Complete WS