Cambridge Additional Mathematics

36 Functions (Chapter 2)

The charges for parking a car in a short-term car park at an airport are shown in the table below. The total

charge isdependenton the length of timetthe car is parked.

Car park charges

Timet(hours) Charge

0 - 1 hours $ 5 : 00

1 - 2 hours $ 9 : 00

2 - 3 hours $ 11 : 00

3 - 6 hours $ 13 : 00

6 - 9 hours $ 18 : 00

9 - 12 hours $ 22 : 00

12 - 24 hours $ 28 : 00

Looking at this table we might ask: How much would be charged forexactlyone hour? Would it be $ 5 or

$ 9?

To avoid confusion, we could adjust the table or draw a graph. We indicate that 2 - 3 hours really means

a time over 2 hours up to and including 3 hours, by writing 2 <t 63 hours.

Car park charges

Timet(hours) Charge

0 <t 61 hours $ 5 : 00

1 <t 62 hours $ 9 : 00

2 <t 63 hours $ 11 : 00

3 <t 66 hours $ 13 : 00

6 <t 69 hours $ 18 : 00

9 <t 612 hours $ 22 : 00

12 <t 624 hours $ 28 : 00

In mathematical terms, we have a relationship between two variablestimeandcharge, so the schedule of

charges is an example of arelation.

A relation may consist of a finite number of ordered pairs, such as f(1,5),(¡ 2 ,3),(4,3),(1,6)g,or

an infinite number of ordered pairs.

The parking charges example is clearly the latter, as every real value of time in the interval 0 <t 624

hours is represented.

The set of possible values of the variable on the horizontal axis is called thedomainof the relation.

For example: ² the domain for the car park relation is ftj 0 <t 624 g

² the domain of f(1,5),(¡ 2 ,3),(4,3),(1,6)g is f¡ 2 , 1 , 4 g.

The set of possible values on the vertical axis is called therangeof the relation.

For example: ² the range of the car park relation is f 5 , 9 , 11 , 13 , 18 , 22 , 28 g

² the range of f(1,5),(¡ 2 ,3),(4,3),(1,6)g is f 3 , 5 , 6 g.

We will now look at relations and functions more formally.

A RELATIONS AND FUNCTIONS

exclusion

inclusion

charge $()

time hours()

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\036CamAdd_02.cdr Thursday, 3 April 2014 3:59:52 PM BRIAN