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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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