How do you know if an input output is a function or not?

Question

I know how to get the domain and the range but no matter what i look up it does not help me understand how to tell if an input output is a function or not!

Answer 1

If each input has only one output, it is a function.  If there is more than one output for the same input, it is a relation, but not a function.  Consider an example:

 

y = x² 

 

This is a function, because for each x there is only one value for y, which is x².

 

Now consider this example:

 

y = √x

 

This is not a function, because for an input x, you can have two output values of y, which are ±√x.  For example, if x = 4, then y = ±2.