Definition:A function (also a ‘mapping’) is a rule where each element in a set
(Domain) relates to/maps onto ONE AND ONLY ONE element of
another set (Range).
Can be illustrated by a graph, table of values, formula, diagram.
f : x  x 1
2
x
x
f(x)
2
5
0
1
-3
1
2
-2
3
10
-1
Domain
Range
Functions
2
f ( x)  x  1
2
x   : x  { 3;  2;  1; 0; 1; 2; 3}
Functions
3
• The 2 depictions above represent “discrete functions”.
• Such a function is made up of specific, defined points (often
integers)
• Alternative form:
“continuous functions”
y  x 1
2
x
Functions
4
Notes:• Be aware of the casual use of the word: ‘function’
• Recall from Matric class the meaning of e.g. f (2)
• Rule of thumb for graphical recognition of a function: the
“vertical ruler test”.
• Any vertical line drawn through the graph of a function
cuts the graph ONLY ONCE
(See the definition above).
Do:- Bk 11, Page 53 Ex 3.1
practice in functions
• Note the following (familiar) “families of curves” (functions?)
Functions
5
Straight Lines
Functions
6
Straight Lines
Functions
7
Parabolae
Functions
8
Hyperbolae
Functions
9
Exponential
Functions
10
Do:- Bk 11, Page 54 Summary
of common functions and their
graphs:- learn for Matric and
APM!
Functions
11