1. Warm UpMar. 12 th  Solve each rational equation or inequality.

2. Homework Answers

3. Graphing Rational Functions You will be able to identify: the domain, the y-intercept, the vertical asymptotes and the end behavior asymptote

4. Parent Graphs

5. Domain  Remember: You can’t divide by zero!  All values that make you divide by zero are undefined so we don’t include them in the domain  Examples:

6. Discontinuities  The values that are not included in the domain cause the graph to be discontinuous – meaning there is a break in the graph  Removeable – Hole – caused by a factor that cancelled out while simplifying  Non-removable – Vertical Asymptote – caused by a factor left in the denominator

7. Holes & Vertical Asymptotes (VA)

8. Discontinuities

10. Y-intercept  To find a y-intercept, plug in x = 0 and simplify.  If 0 is undefined and not included in the domain, then the graph does not have a y-intercept.

11. X-intercept(s)  After simplifying by finding the holes, set the function equal to 0 and solve for x.

12. X-intercept(s)

13. End Behavior Asymptotes ( EBA )  To find the end behavior asymptote simply divide the 2 polynomials… but first, look at the degrees of top and bottom.  Bottom Heavy: degree of the bottom is bigger than the degree of the top  EBA is always y = 0  Equal: degree of the bottom is the same as the degree of the top  EBA is always y = leading coefficient leading coefficient  Top Heavy: degree of the top is bigger than the degree of the bottom  There’s no trick, you have to divide using polynomial division.

14. Examples  Identify the EBA for each of the following:

15. Equations from a Graph…  What are the equations of the asymptotes? Describe the equation of the graph.

18.  What are the equations of the asymptotes?  What is the x-coordinate of the hole? Describe the equation of the graph.

19. PRACTICE Identify the domain, vertical asymptote(s), x- and y-coordinates of holes, and end behavior asymptotes.