1. STROUD Worked examples and exercises are in the text PROGRAMME F10 (6 th Ed) FUNCTIONS (revised 29 Jan 14 – J.A.B)

2. STROUD Worked examples and exercises are in the text Processing numbers: functions incl.Inverse of a function Composition – ‘function of a function’ (Trigonometric functions – to be partially covered later) (Exponential and logarithmic functions – moved into graphs slides) Odd and even functions Limits of functions Programme F10: Functions

3. STROUD Worked examples and exercises are in the text Processing numbers: functions Functions are rules but not all rules are functions Functions and the arithmetic operations Inverses of functions Graphs of inverses The graph of y = x 3 The graph of y = x 1/3 The graphs of y = x 3 and y = x 1/3 plotted together Programme F10: Functions

4. STROUD Worked examples and exercises are in the text Processing numbers Programme F10: Functions A function [in one normal sense] is [intuitively] a process that accepts an input, processes the input and produces an output. If the input number is labelled x and the function is labelled f then the output can be labelled f (x) – the effect of f acting on x. Here the action of the function f is described as ^2 – raising to the power 2. [NB: There is a more abstract notion of function in the branch of maths called set theory.]

5. STROUD Worked examples and exercises are in the text Processing numbers Functions are rules but not all rules are functions Programme F10: Functions A function of a variable x is a rule that describes how a value of the variable is manipulated to generate a value of the variable y. The rule is often expressed in the form of an equation y = f (x) with the proviso that for any single input x there is just one output y – the function is said to be single valued. Different outputs are associated with different inputs. Other rules may not be single valued, for example: This rule is not a function. But y = |x 1/2 | is. [J.A.B.]

6. STROUD Worked examples and exercises are in the text Processing numbers All the input numbers x that a function can process are collectively called the function’s domain. So the domain of the function y = |x 1/2 | is the set of all non-negative numbers. The domain of y = 1/x is the set of all numbers except zero. [J.A.B.] The complete collection of numbers y that correspond to the numbers in the domain is called the range (or co-domain) of the function. EXERCISE [J.A.B.]: what are the ranges of the functions above? Programme F10: Functions