Well this is a little deep, but it's really the only way to explain this correctly without restating the definition like the guy above me did...

The definition of a function is basically a set of points in which each element from some set (these are the independent variables) is UNIQUELY mapped to elements of another set (called the dependent variables). Therefore you cannot have two values from one independent variable.

When you draw a vertical line, and it touches the curve twice, this indicates that one of the independent variables is indeed being mapped to TWO values. That is why the vertical line test works in determining what is not a function

Ok let me recall this from memory,

If it passes through more then 1 point its not a function

if it passes through one poin then it is a function

it's that simple nothing more to it, I believe I'm right, so I hoped this helped.

A function assigns a single value of Y to a value of X (when X is the horizontal axis and Y is the verticle axis). If you had two values of Y for any given X, it would no longer be called a function.

Another way to put it: You can only have one output for each input in a function. X is input, Y is output. The verticle line test tells you how many outputs you have for any given input.

The definition of a function is basically a set of points in which each element from some set (these are the independent variables) is UNIQUELY mapped to elements of another set (called the dependent variables). Therefore you cannot have two values from one independent variable.

When you draw a vertical line, and it touches the curve twice, this indicates that one of the independent variables is indeed being mapped to TWO values. That is why the vertical line test works in determining what is not a function

Ok let me recall this from memory,

If it passes through more then 1 point its not a function

if it passes through one poin then it is a function

it's that simple nothing more to it, I believe I'm right, so I hoped this helped.

A function assigns a single value of Y to a value of X (when X is the horizontal axis and Y is the verticle axis). If you had two values of Y for any given X, it would no longer be called a function.

Another way to put it: You can only have one output for each input in a function. X is input, Y is output. The verticle line test tells you how many outputs you have for any given input.