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

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

Operations on Functions Sum Difference Product Quotient

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

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

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.

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

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:

Example 11:

Example 12:

Example 12 continued:

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

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

Example 13 continued:

Example 13:

Example 14:

Example 15:

Example 16:

Example 17:

Example 18:

Example 19: Estimate the function values from the graph.

Example 19 continued:

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.

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

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