how do you tell whether or not a relation is a function?

Question

anonymous · Answer

If it passes the vertical line test. In other words, 1 x cannot give you more than one y value.

mertsj · Answer

If you have the graph of the relation, use the vertical line test.  If not, use the definition of function which is that no two ordered pairs have the same first number.

anonymous · Answer

okay......thats a bit confusing but i think i understand it a bit better

anonymous · Answer

It is not so much to understand really. We define a function f from a set D to a set Y as a rule that assign a unique (single) element $$f(x)\in  Y$$ to each element $$x \in D$$. So if f is a function with domain D, its graph will consist of the points in the Cartesian plane whose coordinates are the input-output pairs for f. In set notation this is
$$  { (x,f(x))|x \in D }$$. 

Since we have defined the output to be a single and unique element, a vertical line test can be used to determine whether or not a relation is a function. If the graph in the cartesian plane crosses the vertical line twice, it means that there is not only one single unique element of the output values that corresponds to the input values, but two or perhaps more.