Functions can be a hard concept to teach to primary and secondary students! Math Is Fun gives as good of a review as anyone. One of the hardest concepts for students to grasp in when a function is really a function and when it isn’t. If we are lucky enough to have a graph then we may simply use the vertical line test but normally this is not the case, so, let me offer an analogy
Using text messaging for our example here are our definitions using inputs and outputs.
Function: Cell Phone
Input: Cell phone numbers in our address (a)
Output: Sent text messages (TM)
Our Function is thus
TM = f(a)
Text massages are a function of what address we input.
Now we have a platform to teach our function concept. For additional questions, download the worksheet titled What is A Function in the math downloads section