Thursday, November 17, 2011

Functional Graphs

There are some graphs of basic functions that every math student should know. If you can recognize what a function is going to look like when it is graphed on the xy plane, you’ll be a lot more likely to be able to figure out problems about that function, because you’ll be familiar with is.

Think of this – when someone is talking to you about a person, it’s hard to understand exactly what they are taking about, unless you have some kind of mental picture of the person they are talking about. Otherwise, you’ll be saying “Huh?”

So, to help you avoid saying “huh”, I am going to help you learn to recognize the graphs of basic functions.

First, clip_image002[4], the most basic function. And probably the most boring. Blah.


And the next one, clip_image002[6], this is a “parabola” – think “bowl.”



After the parabola, we must have a “cubic”clip_image004 (think, a “cube” has three dimensions – height, width, length)


Next,clip_image006 , also known as the “absolute value function”.


The slightly odd function, clip_image010 - a tricky function, because it is not defined at x=0!


Now for one of my very favorite functions,clip_image008(an “exponential” with the famous number “e” – yes, it is a number.)



And we have have the exponential function without it’s inverse,clip_image012(which is also not defined at x=0)


So there you have it – the seven basic functions (that are not trig functions – we’ll deal with those in another post). If you can memorize what these look like, you’ll be set through almost all of your math years. But I won’t let you get away with just memorizing them. Eventually we’ll study exactly why these functions look the way they do, and we’ll learn a lot of really amazing stuff about them.

Which is your favorite graph? Why?

(ps – I made these graphs using an amazing FREE graph drawing tool for your computer called WinPlot – if you don’t have a graphing calculator, this will be very useful for you. You can do a lot of the same things you can do on a graphing calculator using this program)

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

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