1 Introduction
2 Mathematics is not only about computing
3 Basic concepts
4 Elementary functions
4.1 What is it a function?
4.2 The absolute value
4.3 Lower and upper integer part
4.4 Linear function
4.5 Quadratic function
4.6 Polynomial function
4.7 Roots
4.8 Rational function
4.9 Trigonometric functions
4.10 Exponantiation and logarithm
5 Analytical geometry
6 Warning
7 List of the used symbols
Index
Bibliography
4.8 Rational function
We call rational function any function of the form
\begin{equation*}
f(x) = \frac{P(x)}{Q(x)},
\end{equation*}
where $P$ and $Q$ are polynomials. Generally speaking, the domain of such a function is given by the set of all real numbers that does not contain roots of the polynomial $Q$, i.e.
\begin{equation*}
D_f = \{ x \in \mathbb{R} \mid Q(x) \neq 0 \}.
\end{equation*}
Rational functions include linear, quadratic and all polynomial functions. Simply, you just have to set $Q(x) = 1$, for $x\in\mathbb{R}$ and $P$ to be any polynomial.
It is no longer easy to say something about the image set, so we will not dicuss this question. However, let us at least show a few examples illustrating that there can be very diverse situations (see picture 4.9).
