Question 7763: Can you explain the functions of x better to me? Just started Class and I am not understanding it
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! There are a few things to know about functions.
A function is basically a rule or set of rules that tell you what to do with your input value, in this case, the x, so that you'll have an output value. You can practically think of it as a machine that needs to be fed something, and it does something to what you feed it, and it outputs something based on its inner-workings.
When you hear "function of x" as said exactly like that, all it means is that x is an input, x is to be manipulated, and a new value is to be "popped out". In written form, it will be "f(x)". To be more useful, you'll see it this way: "f(x) = x + 7". This means that there is a function that takes in a value x and adds 7 to it.
A lot of times, they will ask you to find f(1) or f(2) for example. All this means is to plug in 1 or 2 in place of the x on the right side of the equation. For example, let's stick with our example f(x) = x + 7. If they ask you to find f(1), you go "f(1) = 1 + 7 = 8," so you could straight-up write "f(1) = 8" meaning "if you plug in 1 into the function, you get an 8 out." So if you were asked to find f(2), that would be f(2) = 2 + 7 = 9, so f(2) = 9.
Another important thing about functions is that a single x value will only output to one y-value. Let's say that we have a function called "partner" that inputs a guy's name and outputs his partner's name. If "partner" were TRULY a function, then partner(guy's name) = only one girl's name. AKA, a guy can only have one girlfriend for the whole situation to be functional. (Pun intended). HOWEVER! Although a single x value may only output a single value, different x's CAN output the same single value. In other words, thinking about this partner function, a given guy may only have one girlfriend like we said, but another guy CAN also have that same girl. That's where it gets messy in real life, but it's allowed in algebra functions.
That's just the very basics of functions. I hope that helped a bit.
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