Answer:
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 relation 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.
In one semester at college, there is a relation between a student and their final grades; the same student can have different grades in different courses. In a particular class, there is a function from the students to their grades. The professor assigns a grade to each student and each student is assigned one and only one grade.
Generally there is a relation between time and temperature (as in the weather). If you look at a particular location, temperature is a function of time; at any moment the thermometer at that location can only read one temperature.
Once you pull up to a pump and choose your fuel, the cost of filling up your car with gas is a function of how much gas you put in your car. The cost of taking a (particular) taxi is usually a function of how long the ride is.
Step-by-step explanation:
There you go. I hope that helps.
