1. College Algebra Chapter 2 Functions and Graphs Section 2.8 Algebra of Functions and Function Composition

2. Concepts 1. Perform Operations on Functions 2. Evaluate a Difference Quotient 3. Compose and Decompose Functions

3. Operations on Functions Sum Difference Product Quotient

4. Examples 1 – 4: Given,,, evaluate the function, if possible.

5. Examples 5 – 7: Given,,, evaluate the function, if possible.

6. Example 8: Evaluate and write the domain in interval notation.

7. Example 9: Evaluate and write the domain in interval notation.

8. Example 10: Evaluate and write the domain in interval notation.

12. Concepts 1. Perform Operations on Functions 2. Evaluate a Difference Quotient 3. Compose and Decompose Functions

13. The expression is called the difference quotient. Difference Quotient The average rate of change between P and Q is the slope of the secant line and is given by:

14. Example 11:

16. Example 12:

17. Example 12 continued:

19. Concepts 1. Perform Operations on Functions 2. Evaluate a Difference Quotient 3. Compose and Decompose Functions

20. Composition of Functions The composition of f and g, denoted is defined by.

21. Example 13 continued:

22. Example 13:

23. Example 14:

24. Example 15:

26. Example 16:

29. Example 17:

30. Example 18:

31. Example 19: Estimate the function values from the graph.

32. Example 19 continued:

33. Example 20: A party balloon is being filled with helium. As the balloon is filling, the radius of the balloon is changing at the rate of 3 inches per second. a.Write a function that represents the radius of the balloon r(t) after t seconds. b.Write a function that expresses the volume of the balloon V (r) as a function of its radius r.

34. Example 20 continued: c. Evaluate and interpret the meaning in the context of this problem.

35. Example 20 continued: d. Evaluate and interpret the meaning in the context of this problem.