October 05, 2006


This is in response to Mr. K's Blogging Prompt. This will be brief but I'll do my best to state what I think. Here it goes.

Symbolic, numeric and graphical representations of functions are three different ways of showing the same thing. I see them as a part of our 'math arsenal', ready to be used at our disposal. For example, which of the three would we use to describe our journey from Winnipeg to Gimli? We're talking about real life right now.. Are we going to show a graph of our journey? Concavities.. horizontal lines.. Should we show an equation? "Oh hi there John, on my way to Gimli my journey could be described by f(x) = 2x3 ". Imagine someone doing that. I guess not. In this case, I'd show John a chart with my distance in one column, and time on the other. If he sees my distance constantly increasing, he knows im moving. If he sees it become constant, he'd know I stopped. They all represent the same thing, but we use what makes sense given our situation.

How are they different. Well, I'd put it this way. Graphs, equations and numbers are different languages. Equations are precise and general ways of describing values. For example, in the real world, given an equation, when we're given ANY input, we can easily get an output. Graphs. Graphs appeal to our eyes. We 'see' what's being described. I said given an input, we get an output through an equation. We can do the same thing with a graph, but for example, given the graph of f(x) = 1000x + 49. If a person wants to find f(500), MAN that would take a LOOOOONG time to find the answer through a graph. Table of values. They're specifically about inputs and outputs. Given one thing, you get another. Without crossing the boundaries between these media (graphs, equations, t of v), you can't really understand something fully with a table of values. You can precisely say, however, what an input would give you. Just look for it. Okay, getting late. Toodles.

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