4. Process Modeling
4.8. Some Useful Functions for Process Modeling
4.8.1. Univariate Functions
4.8.1.2. Rational Functions

4.8.1.2.1.

Constant / Linear Rational Function

Function:	${\displaystyle f(x)=\frac{{\beta }_0}{1+{\beta }_{1}x},{\beta }_0\ne 0,{\beta }_1\ne 0}$
Function Family:	Rational
Statistical Type:	Nonlinear
Domain:	${\displaystyle (-\mathrm{\infty },-\frac{1}{{\beta }_1})\cup (-\frac{1}{{\beta }_1},\mathrm{\infty })}$
Range:	${\displaystyle (-\mathrm{\infty },0)\cup (0,\mathrm{\infty })}$
Special Features:	Horizontal asymptote at: ${\displaystyle y=0}$ and vertical asymptote at: ${\displaystyle x=-\frac{1}{{\beta }_1}}$
Additional Examples: