Introduction to

functions

19

Contents:

A Mapping diagrams [3.1]

B Functions [3.1, 3.2]

C Function notation [3.1, 3.6]

D Composite functions [3.7]

E Reciprocal functions [3.2, 3.5]

F The absolute value function [1.6, 3.2]

Opening problem

#endboxedheading

A dot is placed at the 20 cm mark of a ruler as illustrated.

Things to think about:

² How far from the dot is the:

I 5 cm mark I 16 cm mark I 20 cm mark I 24 cm mark I 30 cm mark?

² Is there a formula to find the distancedcm between the dot and thexcm mark?

Consider the family of Mr and Mrs Schwarz. Their sons are Hans and Gert and their daughter is Alex.

There are many relationships between members of the family. For example, “is a brother of”, “is older

than”, “is the parent of”, and so on.

Alongside is amapping diagramwhich maps the set of

childrenConto the set of parents,P.

The connection for this mapping is: “is a child of”.

A MAPPING DIAGRAMS [3.1]

cm

0 5 10 15 20 25 30 35

Hans

Gert

Alex

C

Mr Schwarz

Mrs Schwarz

P

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y:\HAESE\IGCSE01\IG01_19\383IGCSE01_19.CDR Wednesday, 8 October 2008 10:19:16 AM PETER