Question

What is an example of a function that describes a situation?

Answer 1

Consider a taxi and the fare you have to pay to go from A street to B avenue and call it `f`.

`f` will depend upon various things but to make our life easier let assume that depends only upon the distance `d` (in km).
So yo can write that "fare depends upon distance" or in mathlanguage: `f(d)`.

A strange thing is that when you sit in the taxy the meter already shows a certain amount to pay...this is à fixed amount you have to pay no matter the distance, let's say, `2$`.
Now for each km travelled the taxi driver has to pay petrol, maintenance of the vehicle, taxes and get money for himself...so he will charge `1.5$` for each km.
The meter of the taxi will now use the following function to evaluate the fare:
`f(d)=1.5d+2`
This is called "linear" function and allows you to "predict" your fare for each distance travelled (even if `d=0`, i.e., when you only sit in the taxi!)
Now, let us assume that the distance `d` between A street and B avenue is `d=10 km`, you fare wiĺ be:
`f(10)=1.5×10+2=17$`

You can now improve your function including additional costs and dependences or build new relationships.