Introduction In this unit, you learned how to use function operations. One of the most important operations is function composition.

Introduction

In this unit, you learned how to use function operations. One of the most important

operations is function composition. Just as two functions, f and g, can be composed

with each other, a function, f, can be composed with itself. Everytime that a

function is composed with itself, it is called an iteration. Iterations can be noted

using a superscript. You can rewrite (f o f)(x) as /2 (x), (f of o f)(x) as f3 (x), and

so on. For this work, it is recommended that you use technology such as a graphing

calculator.

Example 1:

Start with the basic function f(x) = 2x. If you have an initial value of 1, then you

end up with the following iterations.

• f(1)= 2 · 1 = 2

• f^2 (1)=2 · 2 · 1 =4

• f^3 (1) = 2 · 2 · 2 · l = 8

Questions

1. If you continue this pattern, what do you expect would happen to the

numbers as the number of iterations grows? Check your result by conducting

at least 10 iterations.

2. Repeat the process with an initial value of -1. What happens as the number

of iterations grows?

Personal Note: What I noticed is for the second question could it possibly give the answer of negative then positive then negative since for example

f^3(-1) = f^3(-1) * f(-1)?