The connection between factors and zeros are that factors are the factored form of zeros. For example, a zero could be x=2, but the factor would be (x-2). Division helps us factor the polynomials because it helps us break down the factors one by one. If you use synthetic division, you are also able to start with the easy zeros until you find the harder ones through the steps of division. The degree of the polynomial helps us to predict the number of zeros because that number is the amount of times that the line of the graph crosses the x axis. That doesn't always tell us the exact number of factors- it could be less, but it will never be more than that number. That's because the type of graph could only cross the x axis once, meaning that it wouldn't have 5 zero values if 5 was the degree. The number of zeros could be fewer, but not greater, than the degree.
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Even and odd functions are similar in some ways, but there are also a few ways they differ. They're similar because they both require the f(x) formula to equal the f(-x) formula, but different because the f(x) function of an odd formula must also equal the -f(x) function of the equation. To check to see if a function is even, you must find the formula for f(-x). If they match, the function is even. If the functions do not match, you can use the f(-x) function to see if it matches the -f(x) function of the original f(x) function. If the f(-x) and -f(x) functions match, the function is odd. If the f(x) and f(-x) functions or the f(-x) and -f(x) functions don't match, then the f(x) function is neither even nor odd. Even function graphs are always symmetrical over the vertical (y) axis, and odd function graphs are always symmetrical over the origin. I'm not sure if there are any families of functions that are always even or odd, so that is the question I have about this assignment.
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Kayla CampbellArchives
November 2017
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