Learning Resources
Outcomes
In this lesson you will learn
- composition of functions
- the notations f(g(x)) and f o g
By the end of this section students will be able to:
- model problem situations with combinations and compositions of functions
- investigate and interpret combinations and compositions of functions
- analyze relations, functions and their graphs
- use tables and graphs as tools to interpret expressions
Introduction
To date you have done a considerable amount of work with functions. Now you will examine another method of connecting and working with functions called the composition of functions. Actually you have already been composing functions in your earlier work with transforming graphs. Also, in all likelihood, you have used composite functions in some of your science course without even realizing it.
A composite function is formed when two functions are combined so that the range of the first becomes the domain of the second. Through an Investigation in which you find the volume of various sizes of balls, you will come to see just how the composition of functions is done.
The understanding of composite functions is crucial for the study of calculus in such things as the chain rule for finding a derivative of a function. (A topic you will study later).
Please note, for the first investigation, you will need the following supplies.
- 5 different sizes of balls
- a measuring tape or string
- a metre stick
You should require about an hour to complete this section of study.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- domain and range
- algebraic substitution
- how to rearrange formulas
- formula for the circumference of a circle
- formula for the volume of a sphere
- how to sum an arithmetic series (for question #13)
- formula for distance in terms of velocity and time (for question #15)
- Pythagorean Theorem
- how to graph cos2x
- the relationship between logarithmic and exponential functions (for question #17)