In this lesson you will learn
By the end of this section students will be able to:
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.
You should require about an hour to complete this section of study.
To be successful in this lesson, it would be helpful to know the following: