This is because the sign diagram gives us the zeros

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Unformatted text preview: x x is x = 0. By definition, a polynomial has all real numbers as its domain. Hence, g can’t be a polynomial. 3 2. Even though p(x) = x +4x simplifies to p(x) = x2 + 4, which certainly looks like the form x given in Definition 3.1, the domain of p, which, as you may recall, we determine before we simplify, excludes 0. Alas, p is not a polynomial function for the same reason g isn’t. 3. After what happened with p in the previous part, you may be a little shy about simplifying 3 q (x) = x 2+4x to q (x) = x, which certainly fits Definition 3.1. If we look at the domain of x +4 q before we simplified, we see that it is, indeed, all real numbers. A function which can be written in the form of Definition 3.1 whose domain is all real numbers is, in fact, a polynomial. √ 1 1 4. We can rewrite f (x) = 3 x as f (x) = x 3 . Since 3 is not a natural number, f is not a polynomial. 5. The function h(x) = |x| isn’t a polynomial, since it can’t be written as a combination of powers of x (even though it can be written as a piecewise function involv...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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