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:

${\displaystyle f:\mathrm{\hspace{0.5em}\hspace{0.5em}}\{\begin{array}{ccc}\hfill D_f& \hfill \to \hfill & ℝ\hfill \\ \hfill x& \hfill ⟼\hfill & x^k\hspace{0.5em},\hfill \end{array}}$
where $k\in \mathbb{Z}\setminus \{0\}$ and $D_f=ℝ$ for $k\in \mathbb{N}$ as well as $D_f=ℝ\setminus \{0\}$ for $k\in \mathbb{Z}$ 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.