Univariate functions
Introduction
- Definition of univariate function: A function where one variable (usually identified with the letter \(y\)) depends on one other variable (usually identified with the letter \(x\)).
- A function needs not be formulated mathematically. For example, one can show the same relationship with a table (GDP over time example)
- A univariate function can also be represented by a graph on a two-dimensional space (example)
Basic definitions
- Function: Rule assigning a unique value to our dependent variable given the value of the independent variable. Why is it important that the value of the dependent function be unique?
- Domain: All the values taken by the independent variable (usually identified with the letter \(D\))
- Range: All the values taken by the dependent variable (usually identified with the notation , \(f\left(x\right)\) "eff of ex")
Functional notation
- Standard notation for a function is: \(y=f\left(x\right)\), where \(y\) is the dependent variable, \(x\) is the independent variable, and \(f\left(\cdot\right)\) is the rule defining the function
Examples
- \(f\left(x\right)=x^3\), numerical examples