The connection between factors and zeros is that factors are basically zeros! What I mean by this is, if a problem's factored form is (x-3)(x+5)(x+8) the zeros would be 3, -5, and -8. By using division to help us find factors, we can break easily see what a factor is without having to guess and check multiple things. Division also makes it easy to find zeros, which, as I said, will lead you directly to the zeros. The degree of a polynomial tells how many zeros we should initially look for, but it doesn't necessarily tell us the exact amount that we will have. A problem can have repeating zeros that may or may not be accounted for in the equation. Therefore, it won't always tell us how many factors the problem has. Polynomials are a great way to know where to start, but they are not everything. You must always be careful and check your work to know for sure when you have finished with a problem and have arrived at the correct solution.
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I learned a lot from this activity. First and foremost, I learned that there are even such things as "even and odd" functions. I also learned how to tell which is which and the best ways to check my graphs. Even and odd functions are similar in the sense that they both must have two components that equal an identical amount. Some differences however are that to be even a function's f(x) must be equal to f(-x) and to be odd a function's f(-x) must be equal to -f(x). While an even function's graph looks like a mirror image across the y-axis, an odd one will look like a reflection; it will be the same but exactly opposite across the y-axis. To check whether a function is even or odd, simply do the operations that I have listed off above. Some function families that are even are parabolas and lines, and one that is odd is the cubed root function family. My biggest question for this section is if there is any easier way to remember that to find if a function is odd you DON'T use the standard f(x) when comparing variations of the function. |
AuthorPeri Sanderson is a Pre Calc student at MPHS Archives
November 2017
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