Chapter 6 Elementary Functions

Section 6.2 Linear Functions and Polynomials

6.2.8 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.

f1 :  { {0} x 1 x ,

f2 :  { {0} x 1 x2 ,

f3 :  { {0} x 1 x3 ,

etc. Their graphs are as follows.

In particular, the graph of the function

f1 :  { {0} x 1 x

is called the hyperbola.
Generally, for the reciprocal of an arbitrary monomial of degree n a corresponding function of hyperbolic type can be specified.

fn :  { {0} x 1 xn .

Exercise 6.2.14
What is the range W fn of the function fn for even or odd n?

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.