A zero is a solution to a polynomial that can be found by looking at a graph and looking for where is crosses the x-axis, some zeros you cannot find by looking at the graph. A factor is a zero put into an equation, for example a graph has three solutions: -2,1 and 2 the factors would be (x+2),(x-1) and (x-2). Dividing polynomials helps us factor because it can simplifies the polynomial to a squared polynomial and get more solutions that can be turned into factors. The leading coefficient's degree shows us how many zeros to look for when solving polynomials. The degree on the leading coefficient does not tell us how many factors there will be, sometimes a polynomial cannot be factored further and that has to be a factor.
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The even and odd functions have one big similarity and that is the fact that they have symmetry. The two functions do not have the same type of symmetry. Even functions have symmetry over the y-axis and the odd functions have origin symmetry.
There is two ways to tell if a function is either odd or even. One is to look at the graph and see it is symmetric over the y-axis, if it is then it is even. If the graph has origin symmetry then it is an odd function. The second way is to look at the equation. If f(x)=f(-x) then the function is even and if f(-x)=-f(x) then the function is odd. If the function does not follow either of these rules then the function is neither odd nor even. If a function has an even exponent then it can be an even function but it is not guaranteed. If a function has an odd exponent then it can be an odd function but like with the even functions it is not guaranteed. |
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November 2017
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