Chapter 6 Elementary Functions
Section 6.2 Linear Functions and Polynomials6.2.8 Hyperbolas
We consider functions which have a reciprocal relation in their mapping rule. For the determination of the maximum domain of such a function, note that the denominator must be non-zero.
A few examples of reciprocal functions are listed below; these are reciprocals of monomials, and they are also called functions of hyperbolic type.
etc. Their graphs are as follows.
![](../../../images/elfunktionenmtikzauto_40.4x.png)
In particular, the graph of the function
is called the hyperbola.
Generally, for the reciprocal of an arbitrary monomial of degree a corresponding function of hyperbolic type can be specified.
Exercise 6.2.14
What is the range of the function for even or odd ?
Further examples for functions of hyperbolic type were already considered in Example 6.1.12 and in Exercise 6.1.13 in Section 6.1.3.