3 Functions and Series
This chapter gathers together a range of topics relating to functions and their general
properties. Some elementary work on series is also included here, because they most often
arise in the context of expressing or approximating functions.
Prerequisites
It will be helpful if you know something about:- function notation
- plotting graphs
- use of formulae
- inequalities (7
➤
) - sequences and series
- binomial theorem for the case of positive integer power (71
➤
)
Objectives
In this chapter you will find:- function notation and its use
- plotting the graph of a function
- changing the subject in a formula
- odd and even functions
- the composition of two or more functions
- the use of inequalities
- definition and evaluation of the inverse of a function
- definition and use of sigma notation
- summation of a finite geometric series
- summation of an infinite geometric series
- the binomial theorem for negative and fractional exponents
Motivation
You may need the topics of this chapter for:- using formulae in your engineering subjects
- sketching graphs of simple functions (Chapter 10)