Relations are sets of ordered pairs. Usually, the first coordinates come from a set called the domain and are thought of as inputs. The second coordinates are thought of as outputs and come from a set called the range (I actually prefer to call this the co-domain but that’s a long story we don’t need to go into here).

In order for a relationship to be a function, each input must have one and only one output.

So, Five real-world examples:

If you look at a collection of people, you can think of there being a relation between height and age (people generally get taller as they age then remain the same height for a while and then at some point they start getting a bit shorter). This is a relation but not a function because if you input an age people of the same age will have different heights. However, for a particular person, height is a function of age. At any given point in their life (age) that person will be exactly one height. It’s impossible for one person to be 5’ 6” and 6’ 2” at the same time

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