Next Page Previous Page Home Tools & Aids Search Handbook
4. Process Modeling
4.8. Some Useful Functions for Process Modeling
4.8.1. Univariate Functions
4.8.1.2. Rational Functions

4.8.1.2.2.

Linear / Linear Rational Function

examples of linear/linear rational functions
Function: \( \displaystyle f(x) = \frac{\beta_0 + \beta_1x}{1 + \beta_2x}, \ \ \beta_1 \neq 0, \ \beta_2 \neq 0 \)
Function
Family:

Rational
Statistical
Type:

Nonlinear
Domain: \( \displaystyle \left(-\infty, \ -\frac{1}{\beta_2}\right) \ \cup \ \left(-\frac{1}{\beta_2}, \ \infty\right) \)
Range: \( \displaystyle \left(-\infty, \ \frac{\beta_1}{\beta_2}\right) \ \cup \ \left(\frac{\beta_1}{\beta_2}, \ \infty\right) \)
Special
Features:

Horizontal asymptote at:

\( \displaystyle y = \frac{\beta_1}{\beta_2} \)

and vertical asymptote at:

\( \displaystyle x = -\frac{1}{\beta_2} \)

Additional
Examples:
linear/linear rational function example 1: y = (10-7*x)/(1+0.333*x)
linear/linear rational function example 2: y=(0.2+3*x)/(1+x)
linear/linear rational function example 3: y = (-50-3*x)/(1-4*x)
linear/linear rational function example 4: y = (400+1000*x)/(1+0.25*x)
Home Tools & Aids Search Handbook Previous Page Next Page