#### 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:

$f:\mathrm{ }\left\{\begin{array}{ccc}\hfill {D}_{f}& \hfill \to \hfill & ℝ\hfill \\ \hfill x& \hfill ⟼\hfill & {x}^{k} ,\hfill \end{array}$

where $k\in ℤ\setminus \left\{0\right\}$ and ${D}_{f}=ℝ$ for $k\in ℕ$ as well as ${D}_{f}=ℝ\setminus \left\{0\right\}$ for $k\in ℤ$ 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.