Factors and zeroes of a function, or graph, have a connection. If a graph has a zero at 3, then one of the graphs factors will be (x-3), because (3-3)=0. Also, if there is a non-easy zero, then you will have to use some form of division to factor out the rest of the equation. If the equation that needs to be factored, is x^4-x^3-9x^2+3x+18, there will be easy zeroes at -2 and 3. You will then divide the equation by both factors, synthetically, or by long division. Once you have done this, you find the other factor is (x^2-3), and the zero would be the square root of 3. The degree of the polynomial will determine the amount of zeroes. However, this does not affect the number of factors, because in the last example, there were only 3 factors, and the degree was 4.
In the Even and Odd Functions activity, I learned how even and odd functions are similar, how they are different, how to check to see if a function is even or odd, and what families of functions that are always even or odd. Even and odd functions are similar in the fact that on the left of the y-axis, their -x is paired with a y that relates to the y on the right side of the y-axis. The difference is that for even functions, the y is the same, but for odd functions, it is a -y. You can check to see if a function is odd or even by solving algebraically, looking at it graphically, or by looking at the table. There are no families of functions that are always even or odd. I am unsure how to check to see if an equation is odd.
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