1. Warmup Alg 2 6 Mar 2012

2. Warmup Alg 2 7 & 8 Mar 2012

3. Warmup Alg 2 9 Mar 2012

4. Agenda Don't forget about resources on mrwaddell.net Chapter 8: Rational Functions Can you graph simple rational functions?

5. Go over assignment from last class period

6. Section 8.2: Simple Rational Functions and their graphs

7. Vocabulary Domain Range The places along the x axis where the graph lives The places along the y axis where the graph lives

8. Vocabulary Rational Expression Asymptote Vertical Horizontal A quotient of 2 polynomials An invisible line that the graph gets close to, but never touches.

9. Vocabulary Vertical AsymptoteOccurs anywhere the fraction is divided by zero. You must, MUST, MUST check to find out where the denominator equals zero. This is NOT optional.

10. Checking for Vertical Asymptotes Is this a Rational function? Yes, the numerator is cubic, the denominator is linear Where does the denominator equal zero? 6x Take the bottom = 0 Set it equal to zero and solve. x = 0 There is a vertical asymptote at x = 0

11. Checking for Vertical Asymptotes Is this a Rational function? No, the 2 x messes it up!

12. Finding the domain What is the domain of the expression? Where does the denominator equal zero? 6x -12Take the bottom= 0 Set it equal to zero and solve. 6x = 12 There is a vertical asymptote at x = 2 x = 2 The domain is: All Reals except x = 2

13. Graphing Simple Rational Functions The parent function for all rationals. Where does the denominator equal zero? xTake the bottom= 0 Set it equal to zero and solve. There is a vertical asymptote at x = 0 The domain is: All Reals except x = 0

14. x= 0 is the vertical asymptote, and y=0 is the horizontal asymptote The domain is all reals and x ≠ 0 The range is all reals and y ≠ 0

15. Textbook notes

16. x= 0 is the vertical asymptote and y =0 is the horizontal asymptote. The domain is all reals except x = 0 The range is all reals except y = 0

17. x= 0 is the vertical asymptote and y = 0 is the horizontal asymptote. The domain is all reals except x = 0 The range is all reals except y = 0

18. x= 0 is the vertical asymptote and y = 0 is the horizontal asymptote. The domain is all reals except x = 0 The range is all reals except x = 0

19. Graphing Simple Rational Functions What does the “a” do to the equation? How did the graphs change as “a” went from 1 to 12? Just like all the other translations, “a” makes it skinny or fat, and a negative “flipped it” around the X AXIS.

20. Graphing Simple Rational Functions What do you think the “h” and the “k” do to the graph? If you said, “The same thing as with radicals and quadratics and polynomials,” you are RIGHT! “h” moves it left and right, (but opposite to the sign” and “k” moves it up and down!

21. Textbook notes

22. x= -3 is the vertical asymptote and y = 0 is the horizontal asymptote. The domain is all reals except x = -3 The range is all reals except x = 0

23. x= -3 is the vertical asymptote and y = 4 is the horizontal asymptote. The domain is all reals except x = -3 The range is all reals except x = 4

24. Graphing Rational Functions Now they are a little more complex. The numerator and denominator are both lines, that is very important. The vertical asymptote is at x = -d/c The horizontal asymptote is at y = a/c

25. x = 4 is the vertical asymptote y=2 is the horizontal asymptote. The domain is all reals except x = 4 The range is all reals except y = 2/1 = 2

26. Textbook notes

27. Assignment Section 8.2: 11 – 18, 29 – 34