Sunday, September 18, 2011
Summarize 3B
Can you summarize something we learned so far into one nice paragraph for people to use? For example can you summarize functions transformations, or even and odd functions. Keep in mind I am not asking you to summarize how to do things, but give a total picture of what even and odd functions, and then how to determine them. Be holistic here.
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even functions are symmetric to the y-axis. odd functions are symmetric to the origin (x axis). a function is neither when you plug in -x for x and don't get f(x) or -f(x). to figure out whether a function is odd or even you should plug in -x for all of your x's and simplify it. if you get the same thing you stared with then it is even. if you get the exact opposite of what you started with then the function is odd. and if you get neither one of those then the function is neither. i hope this was helpful!
ReplyDeleteOne of the things we've learned is properties of graphs, and though some of the properties were review, others were new. But since there's quite a few, I chose to describe increasing and decreasing intervals. Hope this helps!
ReplyDelete•Increasing Intervals are what the x-values are when the y-values are increasing. In the graph, it comes up as a diagonal line going up from left to right.
•Decreasing Intervals are what the x-values are when the y-values are decreasing. And in the graph, that would be a slanted line going down from left to right.
For transformations,we've learned about vertical/horizontal stretch and vertical/horizontal shrink. The vertical stretches and shrinks function for the graph is y = af(x). The graph transormation either gets taller or shrinks. It stetches vertically only if a>1. If a<1 but greater than 0, then it is a vertical shrink. So look out for the # in front of f(x) to determine if it is a vertical stretch or shrink.
ReplyDeleteA horizontal stretch and shrink is like the opposite of the vertical stretch/shrink. This time it streches or shrinks from left to right. Their function is y=f(cx). It will stretch if 01. Oh and dont forget to use the recipricol.
Oh, and in the last sentence I ment to say it will stretch if 0 < c < 1. It will shrink if c > 1
ReplyDelete..my bad.
We've recently learned about standard position angles. It's a very simple concept. If an angle has a positive degree, it rotates counter-clockwise. For an angle with a negative degree, it rotates clockwise.
ReplyDeleteDuring this time we learned whether functions were even or odd. One easy way to figure this out was to see whether the exponents in the function were all odd or all even. If the exponents were all even, then the function would be even. If the exponents were all odd, then it would be a odd function. If there was a mix of both, then the function would be neither. You could also do the f(-x) of the function, and if the function turns out exactly the same the function is even, if the function turnt out the exact opposite then it would be odd, and if there were some the same and some opposite then the function would be neither.
ReplyDelete