1. Section 8.1 Composition of Functions

2. Consider the following two functions:
What is f(4)?
What is g(8)?
Let’s say we define a function h such that h(4) = 21, what is the rule for h?
In general we have h(x) = g(f(x))
Find h(2) and h(6)
What if we have k(x) = f (g(x))
Find k(2) and k(6)

3. Using the same two functions:
Let’s find algebraic rules for h(x) = g(f(x)) and k(x) = f (g(x))
Using your new functions find h(2), h(6), k(2) and k(6)

4. In your groups see if you can fill in the following table
Inputs 1 2 3 4 5
Outputs for f
Outputs for g
Outputs for g composed with f
Outputs for f composed with g
Outputs for f composed with f

5. Using the graph find f(g(2)) and g(f(1.6))

6. Example
Suppose that oil is leaking out of a damaged tanker. The oil is forming a circular-shaped slick on the surface of the water. Suppose that the radius t hours after the leak began is given by r = f(t) = 300t meters. Note that the area of a circle is a function of its radius given by A = g(r) = πr2. What does g composed with f represent?
Find a formula for the area of the slick t hours after it spilled.
For how many hours has it been leaking to have an area of 10,000,000 square meters?

7. In your groups try problems 5, 13, and 28