What is a function?

Question

Can someone explain to me what a function is?

Also, which of the following is a function?
1) xy = 7
2) x = 7
3) x^2 - y^2 = 7
4) x^2 + y^2 = 7

I thought it was 2 because isn't a function "For every value of x, there is only one value of y" ? or is 7 not y?

Answer 1

When a vertical line is passed through a function it will cross only 1 point (vertical line test). So x =7 is not a function (because it is a vertical line) but xy=7 is because it can be rewritten as y= 7/x, only one answer for each x.
The next two can't be because they have two solutions which mirror each other, so two y's per x. For example, if x is -1, y will be +2.45 and - 2.45 for problem 4.

Answer 2

A function is just an expression of how the value of one variable depends upon the action of another (or, several other) variables.

2) above is not really a function since the action of x has no bearing on y's value.

Answer 3

a function is a relation where for every input value (x), there exists no more than 1 output value (y)

would you like a complete discrete definition?

1 is a function

Answer 4

Go to this reference:

functions.wolfram.com/ - 22k

HANK (Josh)

Answer 5

check a dictionary! or and online one! i hope you find it out idk!