It was a cold, cloudy, and windy morning on the seventh of September and in the depths of room 215 Mr.B was challenging the mathematical intelligence of his student’s with the question “What is a Function ?”. On his “smart board” he posted this question of epic proportions along with several line graphs below it which he wanted his student’s to determine as either functions or non-functions.

“Get to work”, Mr.B ordered and the class went about organizing the several line graphs accordingly. Some people organized these graphs into function or non-function groups on their own, while others talked within their group and then made their decisions. But after the time was up mostly everyone had classified their graphs into the same groupings which seemed to disturb and disappoint Mr. B, who saw many errors of this organization. So as a class we began to analyze and discuss which groupings each of the six graphs belonged in.

First there were 2 graphs with a single parabola. One of these parabola graphs made a “U” shape on its linear plane, while the other made a backwards “C”. These were easy to decide on and as a class we determined that both of these were “functions” right off the bat. Then there was a graph with an oval in it called an “ellipse”. As a class we debated on whether or not this was a function along with another graph that had not only a “U” shaped parabola but also a straight line graphed near the bottom left. Then there was a “hyperbola” graph, I believe, that made an “S” shape on its side. The class also determined this to be a function. Then lastly came the awkward graph of the group. Many considered this graph to be a “non-function” due to the line’s sudden sharp corner it had that completely went off in a different direction in the middle of the linear plane. That meant that this line would not have a proper equation to represent it as a whole. When asked why we made these choices of classification, some (like me) thought that a function could only be a graph which lines corresponded to one equation for each line, or something to that nature. But then Mr.B showed us the light by saying “The definition of a function is not an equation, the true definition of one is a relationship between 2 variables.” This opened our eyes and using this information we reorganized the graphs correctly into function and non-function groups. Some student also said that with a function “if you were given ‘x’ then you can also find ‘y’”, which is very true. Then Mr.B concluded before the bell rang, “In a function when given an input variable there’s only one output variable.”

So in the end (the end of class that is) we gathered the information meant to be taken from this lesson, and we walked out of Pre-Cal class knowing how to define a function and identify one.