Equation: A mathematical problem in which two expressions are equal. For example, 5 + 5 = 10 is an equation, as is x + 5 = 10.
Function: A mathematical equation where there is only one output for each input. For example, y = x + 1 is a function, because each input (whatever number you put in for x) results in only one output (the number y will equal). You can check to see if an equation is a function by graphing it. When you graph a function, no vertical line will hit more than one point from the function. If a vertical line goes through more than one point, then the graph does not show a function.
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Matt,
I think you were the only one who mentioned the vertical line test. I feel that this should have also been part of my definition since we place so much emphasis on this test when we ask our students to decide if a graph is a function.
It also gets to the skill we want students to have: to tell the difference between relationships that are functions and relationships that are not functions.
Nathan