College Algebra Chapter 2 Functions and Graphs Section 2.8 Algebra of Functions and Function Composition Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Concepts Perform Operations on Functions Evaluate a Difference Quotient Compose and Decompose Functions

Concept 1 Perform Operations on Functions

Perform Operations on Functions

Examples 1 – 4 (1 of 2)

Examples 1 – 4 (2 of 2)

Examples 5 – 7

Example 8 Evaluate and write the domain in interval notation.

Example 9 Evaluate and write the domain in interval notation.

Example 10 Evaluate and write the domain in interval notation.

Skill Practice 1

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

Skill Practice 3

Concept 2 Evaluate a Difference Quotient

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

Example 11

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

Example 12

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

Concept 3 Compose and Decompose Functions

Compose and Decompose Functions

Example 13

Example 14

Example 15

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

Example 16

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

Skill Practice 8

Skill Practice 9

Example 17

Example 18

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

Example 19 (2 of 2)

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.

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 balloon @ time t.

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 904.32 cubic inches.

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.

Skill Practice 11

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.