1. Warm up 1. Find f(6). 2. Find g(2). 3. Given r(x) = 2x – 1, evaluate the domain {0, 1, 2, 3}. What is the range of r(x)? 4 -2 Range: {-1, 1, 3, 5}

2. Review HW

3. Skills Check Pencil & calculator only When finished, flip it over, and sit quietly.

4. UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems? Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5 Essential Question: What is an exponential function and how is different from a linear function? What does their point of intersection represent?

5. Exponential Functions

6. First, let’s take a look at an exponential function xy -21/4 1/2 01 12 24

7. So our general form is simple enough. The general shape of our graph will be determined by the exponential variable. Which leads us to ask what role does the ‘a’ and the base ‘b’ play here. Let’s take a look.

8. First let’s change the base b to positive values What conclusion can we draw ?

9. Next, observe what happens when b assumes a value such that 0<b<1. Can you explain why this happens ?

10. What do you think will happen if ‘b’ is negative ?

11. Don’t forget our definition ! Can you explain why ‘b’ is restricted from assuming negative values ? Any equation of the form:

12. To see what impact ‘a’ has on our graph we will fix the value of ‘b’ at 3. We are going to look at positive values of a today. What does a larger value of ‘a’ accomplish ?

13. Shall we speculate as to what happens when ‘a’ assumes negative values ? Let’s see if you are correct !

15. Our general exponential form is “b” is the base of the function and changes here will result in: When b>1, a steep increase in the value of ‘y’ as ‘x’ increases. When 0<b<1, a steep decrease in the value of ‘y’ as ‘x’ increases.

16. We also discovered that changes in “a” would change the y-intercept on its corresponding graph. Now let’s turn our attention to a useful property of exponential functions.

17. Linear, Exponential, or Neither

18. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 1. Linear

19. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 2. Rounds of Tennis12345 Number of Players left in Tournament 64321684 Exponential

20. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 3. This function is decreasing at a constant rate. Linear

21. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 4. A person’s height as a function of a person’s age (from age 0 to100). Neither

22. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 5. Linear

23. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 6. Each term in a sequence is exactly 1/3 of the previous term. Exponential

24. INTERSECTIONS OF GRAPHS

25. Points of Intersection

26. LINEAR VS. EXPONENTIAL FUNCTIONS TASK Classwork

27. Option 1: You can have $1000 a year for twenty years. Option 2: You can get $1 the first year, $2 the second year, $4 the 3 rd, doubling the amount each year for twenty years. Which option gives you more money?

28. RAKING LEAVES TASK Classwork

29. 1. Two dollars for each bag of leaves. 2. Or two cents for one bag, four cents for two bags, eight cents for three bags, and so on with the amount doubling for each additional bag. 1.If Celia rakes five bags of leaves, should she opt for payment method 1 or 2? What if she rakes ten bags of leaves?

30. 1. Two dollars for each bag of leaves. 2. Or two cents for one bag, four cents for two bags, eight cents for three bags, and so on with the amount doubling for each additional bag. 2. How many bags of leaves does Celia have to rake before method 2 pays more than method 1?

31. 1. Two dollars for each bag of leaves. 2. Or two cents for one bag, four cents for two bags, eight cents for three bags, and so on with the amount doubling for each additional bag. 3. Describe the differences in payment plans.

32. 1. Two dollars for each bag of leaves. 2. Or two cents for one bag, four cents for two bags, eight cents for three bags, and so on with the amount doubling for each additional bag. 4. Describe the difference in the way the payment grows in the table and on the graph.

33. 1. Two dollars for each bag of leaves. 2. Or two cents for one bag, four cents for two bags, eight cents for three bags, and so on with the amount doubling for each additional bag. 5. Is this growth situation continuous or discrete? How do you know?

34. TALK IS CHEAP TASK Homework