Chapter 6 Elementary Functions

Section 6.3 Power Functions

6.3.1 Introduction

In Section 6.2.6 and Section 6.2.8 we studied monomials and functions of hyperbolic type. In summary, these can be described as the following type of functions:

f:  { Df x xk ,

where k{0} and Df = for k as well as Df ={0} for k with k<0. In this section, we will allow arbitrary rational for the exponent in the mapping rule. This results in so-called power functions that again include monomials and functions of hyperbolic type as special cases. We will collect their fundamental properties and see some applications.