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C3 Edexcel Maths Help

I just cannot get my head around functions and mappings and domain and range, i just don't get it, even the basic stuff. Someone please please help explain it to me in full!!!
Original post by SSD07
I just cannot get my head around functions and mappings and domain and range, i just don't get it, even the basic stuff. Someone please please help explain it to me in full!!!


Are there any particular questions you're stuck on?

You may like to think of a function as a machine in a factory.

There are certain things that you can put in the machine, which is the domain (think ingredients/materials). You get out certain stuff from each ingredient (maybe car parts or something).

The rules are as follows:

Everything in your domain must be able to fit in the machine and get something out. For example, if we said the 'function' was (1/x), and we said the domain was the numbers (-1,0,1) then it's not actually a function - because 1/0 will break the machine. Even though -1 and 1 will give you sensible products, not EVERY element in the domain will give you an output, which is why it is not a function. If we changed the domain to (-1,1) then you can put everything into the equation, so it is a function as long as it satisfies the next condition.

The other condition is that for anything you put in, you must get exactly one thing out. If you put in a sheet of gold into a machine and got out a gold watch and a silver watch, that wouldn't make sense. The same way, if you put x=1 in for example, and you get out y=5 and y=3, both from x=1 then it's not a function. However, if you put in a gold cube or a gold cylinder and get a gold watch out both times, that's fine.

An example of something that isn't a function is x=y^2. x^2 = y, on the other hand, is fine. It's okay for one y value to have many corresponding x values, but not for one x value to have many y values.
(edited 8 years ago)
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math42
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Basically what a function does is take an "input" value and do something to it, giving you an output.
"mapping" is, if I remember correctly, basically the process of turning this input into the output -we say the input is "mapped" to the output.
Typically we have our input as x and our output as y - you have been using functions for ages, just without much consideration of the technicalities.
y is a considered a function of x, and this is denoted by f(x) = y (but not necessarily - you can have any letter for a function, typically g(x) and h(x) will also be used, but these mean the same thing).
y = 7x and y = lnx are functions, for instance (but they need to be clarified by a domain, which I'll discuss next)

The domain tells you all the input or x-values. For instance, you could have a domain x > 0, -1 < x < 1, or a domain across all real numbers.
The range shows you the lowest and highest points of your outputs or y-values. If the function approaches a certain point - for instance, y = 1/x approaches 0 as x gets very large - then you of course don't have a technical lowest/highest value so you use a strict inequality, i.e. < as opposed to </=
Sometimes the range is infinite; in this case you can use f(x) 3 R (but with the 3 backwards) which is just a fancy way of saying that the function of x spans all the real numbers.

edit: forgot to discuss the difference between "function" and "not a function" but SeanFM's explanation is nice
(edited 8 years ago)
Original post by SSD07
I just cannot get my head around functions and mappings and domain and range, i just don't get it, even the basic stuff. Someone please please help explain it to me in full!!!


Think about domain as the possible values you can substitute in [on the sketch it's the x-axis]

The range is the values the function gives [on the sketch it's the y-axis].

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