1. College Algebra Chapter 2 Functions and Graphs
Section 2.8
Algebra of Functions and Function Composition
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2. Concepts Perform Operations on Functions
Evaluate a Difference Quotient
Compose and Decompose Functions

3. Concept 1 Perform Operations on Functions

4. Perform Operations on Functions

5. Examples 1 – 4 (1 of 2)

6. Examples 1 – 4 (2 of 2)

7. Examples 5 – 7

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

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

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

11. Skill Practice 1

12. Skill Practice 2
Use the function defined in Example 2 to find

13. Skill Practice 3

14. Concept 2 Evaluate a Difference Quotient

15. Evaluate a Difference Quotient
The average rate of change between P and Q is the slope of the secant line and is given by:

16. Example 11

17. Skill Practice 4 Given f(x)=4x-2, Find f(x + h).
Find the difference quotient,

18. Example 12

19. Skill Practice 5
Find f(x + h).
Find the different quotient,

20. Concept 3 Compose and Decompose Functions

21. Compose and Decompose Functions

22. Example 13

23. Example 14

24. Example 15

25. Skill Practice 6
Refer to function f and g given in Example 6. Find

26. Example 16

27. Skill Practice 7
Write a rule for each function and write the domain in interval notation.

28. Skill Practice 8

29. Skill Practice 9

30. Example 17

31. Example 18

32. Example 19 (1 of 2)
Estimate the function values from the graph.

33. Example 19 (2 of 2)

34. Example 20 (1 of 3)
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.
Write a function that represents the radius of the balloon r(t) after t seconds.
r(t) = 3t
Write a function that expresses the volume of the balloon V (r) as a function of its radius r.

35. Example 20 (2 of 3) is the volume of the balloon @ time t.
and interpret the meaning in the context of this problem.
is the volume of the time t.

36. Example 20 (3 of 3)
and interpret the meaning in the context of this problem.
After 2 seconds, the volume of the balloon will be approx cubic inches.

37. Skill Practice 10
An artist shops online for tubes of watercolor paints. The cost is $16 for each 14-mL tube.
Write a function representing the cost C(x) (in $) for x tubes of paint.
There is a 5.5% sales tax on the cost of merchandise and a fixed cost of $4.99 for shipping. Write a function representing the total cost T(a) for a dollars spent in merchandise.
and interpret the meaning in context.
and interpret the meaning in context.

38. Skill Practice 11

39. Skill Practice 12
Refer to the functions f and g pictured in Example 12. Evaluate the functions at the given values of x if possible.