Graph of a function

So why can't a graph of a function have multiple y values per x, while multiples x's per y seems fine? Wtf is this shit?

You know you can raise your hand and ask your math teacher, right? That's what they're paid to do, kid.

Otherwise:
http://en.wikipedia.org/wiki/Function_(mathematics)

Still it just seem rather arbitrary. Like y=|x|, why not x=|y|? What difference do the axes of a graph make?

>>3
A function is simply an equation with exactly one output (y) for every input (x). That's all a function is. What the fuck is so hard to understand?

It's like saying you don't understand why a rectangle isn't always a square.

E = MC²

>>1
It just has to be a function of y, not a function of x.

You can also have the graph of an equation with multiple y values per x and multiple x values per y.

e.g. x^2 + y^2 = 1


The thing is, if you have a function, it has to have an input and give an output.

Now two inputs can correspond to the same output, but if two outputs corresponded to the same input, how would you choose what the value of the function was at that input? It makes no sense (well in the traditional sense of a function, see multifunction)

A function is just a mapping between sets. Bijectivity is not part of the definition, nor is the number of arguments.

This board...

>>4
This is an appropriate analogy.

>>6
>>7
OP is obviously in middle school at best and is too dense to look up a definition in his textbook or ask his teacher. You guys are going a bit over his head without actually setting him straight. You fail harder than anyone else here. Except possibly me because I'm just a troll.

As everybody else pointed out, functions have that property by definition; herp derp

I think what you're trying to ask is, why not consider a more general class of "functions"?  If you lrn2 wiki, then you'd find:
http://en.wikipedia.org/wiki/Multivalued_function
http://en.wikipedia.org/wiki/Relation_(mathematics)

Math is a lot more general than you think; just because it's not taught doesn't mean it's not considered.  Multivalued "functions" most often crop up as inverses (inverse functions are often very important) of noninjective (not 1-1) functions (eg sin, x^2...).  It just so happens that such entities are a hueg pain in the ass.  If you've ever worked with complex logs, you'd know what I mean.

This is also important in computers, where determinism is important.  You want the computer to spit out 1 when you ask for the 4th root of 1.  If it sometimes spits out -1, or +-i, your code is bound to break.

>>10
>>6
Wow, helpful replies, I'm shocked.

So while we're on the topic of stupid questions...
I read log-base-b(b) = 1 and log-base-b(1) = 0. What about log-base-1(1)? 1 or 0? Or log-base-i(1)? 0 or 4?

log_1 (x) would naturally defined to be the inverse of f(x) = 1^x which doesn't exist. log_1 (x) is meaningless.

log_i (x) similarly would be the inverse of g(x) = i^x which doesn't exist. (g(x) is itself multivalued unless you restrict it appropriately)

>>11, 12
I think the standard way is to define Ln first.
My complex analysis book defines the "function" as mapping real numbers -> sets of real numbers: Ln(x) = {y | e^y = x} [which is why e^x is so important; this function is in turn defined by its taylor series]

Then, we can define log_b(x) = Ln(x)/Ln(b)

As I said earlier, complex logs are not "functions" in the traditional sense, which is why they are a huge pain in the ass, unless you love sets.