notes - relations

• meaning of relation (set of ordered pairs)
• different representations of a relation (table of values, cartesian graph, mapping diagram, equation, inequation)
• four types of relation (1:1, n:1, 1:n, n:n)

• meaning of function (n:1 or 1:1 relation)
• a function as an input-output machine
• function notation
• vertical line test

notes - inverse relations and inverse functions

problems sheet - composite functions, inverse relations, inverse functions

QuickMath graph plot

• single equation (1:n and n:n relations allowed)
• more than one equation (1:n and n:n relations allowed)
• single inequality
• more than one inequality

• two and three dimensional graph plotter with animation feature
• For 1:n and n:n relations, select Window/2-dim and Equa/0=f(x,y)...
• Winplot Tutorial

addition of functions
Recognise the graph of f(x)+g(x) ...

multiplication of functions
Recognise the graph of f(x)g(x) ...

composition of functions - software
This slide show shows how f(g(x)) can be constructed graphically from the graphs of f(x) and g(x). It also shows how the chain rule f(g(x))'=f'(g(x))g'(x) can be obtained graphically using this construction.

inverse function
Recognise the graph of f ^-1(x) ...

transformation of graphs
Recognise the graph of f(-x), 2f(x), f(x-1) ...

Field Guide to Functions - CalculusQuest

Functions as Models - StudyWorks Online
Mathematics can be used to “model” the natural world. Functions can serve as very simple mathematical models.

resources page -algebra