1. Chapter 4: Exponential and Logarithmic Functions Section 4.1 Composite Functions Objectives: 1) Notation of Composite Functions 2) Form a Composite Function a ) Evaluate a composite function 3) Find the domain of a composite function

2. Suppose the oil from the Gulf oil leak is spreading in the approximate shape of a circle. If the radius r (in feet) at time t is determined to be: Find the area of the oil slick as a function of time. 1. Composite Functions

3. Given two functions f and g, the composite function is defined by Composite Functions In the previous example: In the previous example: Read as: “ f of g of x ” Meaning: Evaluate “inner” function first. Plug into “outer” function next.

4. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7

5. #11 on back of handout. Now look at graph and answer : #12

6. Rules for excluding numbers from the domain of a composition function 1. If x is not in domain of inner function, it is not in domain of composition function. 2. Any x for which inner function is not in domain of outer function. Determine domain of: Your turn: Determine domain of: