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:
\( \displaystyle f(x) = \frac{\beta_0}{1 + \beta_1x}, \ \ \beta_0 \neq 0, \ \beta_1 \neq 0 \)
Function
Family:
Rational
Statistical
Type:
Nonlinear
Domain:
\( \displaystyle (-\infty, \ -\frac{1}{\beta_1}) \ \cup \ (-\frac{1}{\beta_1}, \ \infty) \)
Range:
\( \displaystyle (-\infty, \ 0) \ \cup \ (0, \ \infty) \)
Special
Features:
Horizontal asymptote at:
\( \displaystyle y=0 \)
and vertical asymptote at:
\( \displaystyle x = -\frac{1}{\beta_1} \)
Additional
Examples: