Thinking about Functions
Rich example

What relation are you?
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Diagrams

We are now going to try to draw diagrams that represent the situations we have just thought about. If we return to our example, we asked ‘What colour is the car?’ about all the cars in the UK.

To represent this, we will take our input (all the cars in the UK) and our output (colours), and represent them by the dots in the diagram below.

An oval labelled cars with 6 dots inside next to an oval labelled colours with 3 dots inside

Of course we are not actually showing all cars, or all colours, but rather a representation of the situation.

Now if we think about the answers we gave to the three questions, we might draw one of the following:

Is there always an answer?

Yes, every car must be a colour of some kind (even if it is multi-coloured).

Could there be multiple answers for each person/place/number?

This depends on what we think about cars that have more than one colour. We could say, no there is only one answer for each car, by including a ‘multi-coloured’ category. Or we could say, yes some cars are more than one colour.

Could different people/places/numbers have the same answer as each other?

Yes, for example lots of cars are red.

all dots which represent cars are matched to one dot representing colour, some cars match to the same colour
Cars map to one colour only, and no cars are left out. (Includes a ‘multi-coloured’ category)
Some dots which represent cars are matched to more than one dot representing colour
Cars map to more than one colour. (No ‘multi-coloured’ category)

Try to draw similar types of diagrams for the situations you have thought about. We have provided diagrams below that may be helpful. Some may match a situation and some may need to be modified.

Once you have a diagram for each situation, look at the different features of each diagram.

  • What do you notice?
  • Are there similarities/differences between the situations?
  • Can any of them be grouped together because they have certain features?

To explore these groups, look at the next section.

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Last updated 14-Jun-17
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