1. Properties of Exponential Functions

2. Warm Up 1. Label the following sequences as arithmetic or geometric then find the next term:  3, -6, 18, -36  10, 6, 2, -2, -6 2. Create a function to model the geometric sequence: 5, 10, 20, 40,… Then find the 10 th term.

3. Homework Questions?

4. From yesterday… Can we generate the terms of the sequence a n = 2(2) n-1 ? TermSequence 1st 2nd 3rd 4th 5th

5. The graph… We graph the order of the term for “x” and the number in that spot for “y” Term X Sequence Y Point 1st1(1,1) 2nd2(2,2) 3rd4(3,4) 4th8(4,8) 5th16(5,16)

6. Let’s graph a n = 16(.5) n-1 We graph the order of the term for “x” and the number in that spot for “y” Term X Sequence Y Point 1st 2nd 3rd 4th 5th

7. You try: a n = 1(3) n-1 We graph the order of the term for “x” and the number in that spot for “y” Term X Sequence Y Point 1st 2nd 3rd 4th 5th

8. THINK/PAIR/SHARE What do these graphs have in common? How are they different? THINK silently for 30 seconds PAIR discuss with your partner for 30 seconds SHARE with the class

9. Exponential Functions Geometric sequences are a type of exponential function. An exponential function is a function with a variable in the exponent. y = a(b) x Just like with geometric sequences, a is the starting value (or y- intercept). b is called the base.

10. Graphing Exponential Functions Today we will graph exponential functions by creating a table of values. Tomorrow we will see how we can graph exponential functions just by looking at the equation.

11. y = 3(2) x XY 0 1 2 3 -2

12. y = -8(.5) x XY 0 1 2 3 -2

13. You try: y = -1(2) x XY 0 1 2 3 -2

14. Characteristics of Exponential Functions Many of the characteristics that we found of linear and quadratic functions still apply to exponential functions. ◦ Y-intercepts ◦ X-intercepts (solutions, zeros) ◦ Exponential functions do not have vertices/minimums/maximums

15. Example: Where are the x- and y-intercepts?

16. You try:

17. Asymptotes Exponential functions also have horizontal asymptotes. These are imaginary lines that the function approaches (gets close to), but never actually touches.

18. Example: Where are the horizontal asymptotes?

19. You try:

20. Group Graphs! Work with your group to create a table of values for the function that I give you. Then use the table of values to sketch a graph of the function. Label the x- and y-intercepts of the function. Make it visually appealing so that I can put it on the wall! Let me know when your group is finished and I will give you your participation stamps for the day.

21. Let’s compare exponential functions and linear functions: y = 2 x XY -2 0 1 2 3 XY -2 0 1 2 3 What do you notice about these two functions?

22. Your soccer team wants to practice a drill for a certain amount of time each day. Which plan will give your team more total practice time over 4 days? Over 8 days? Explain your reasoning.

23. Graph the function f(x) = 2x – 3 Graph the function y = 2 x Compare the two functions.

24. Homework P. 215 (1-12)