Chapter 4: Root, Radical and Power Functions

In Sections 1.2, 1.3 and 1.4, we studied constant, linear, absolute value, and quadratic functions. Constant, linear and quadratic functions were specific examples of polynomial functions, which we studied in generality in Chapter 2. Chapter 2 culminated with the Real Factorization Theorem, Theorem 2.18, which says that all polynomial functions with real coefficients can be thought of as products of linear and quadratic functions. Our next step was to enlarge our field of study to rational functions in Chapter 3. Being quotients of polynomials, we can ultimately view this family of functions as being built up of linear and quadratic functions as well. So in some sense, Sections 1.2, 1.3 and 1.4 along with Chapters 2 and 3 can be thought of as an exhaustive study of linear and quadratic functions. We now turn our attention to functions involving radicals which cannot be written in terms of linear functions. For a more detailed review of the basics of roots and radicals, we refer the reader to Sections A.2 and A.13.