Stitz-Zeager_College_Algebra_e-book

# This is because the sign diagram gives us the zeros

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online