Question

how do you identify a function?

Answer 1

well equation-wise...it's y = x or f(x) = x <---that means that y has no exponents..just plain old y

graph-wise...draw vertical lines on your graph...if it touches only one point on the graph it is a function

function

not a function

Answer 2

Another way to think about a function is that it is a collection of ordered pairs. You can talk about these ordered pairs as \((a,b)\), where \(a\) and \(b\) are numbers. To be a function, this collection of ordered pairs has to have one property. For every \(a\), there can only be one \(b\). Basically, a function "maps" each \(a\) value to a \(b\) value. It can't map the same value to two different values, or it isn't a function.

Another picture you can use to visualize a function makes this mapping relationship a bit more explicit: The top picture is a function, the bottom picture is not. Basically, you can see the function is taking each \(a\) value and assigning it to a \(b\) value, and there can only be one \(b\) for each \(a\).