Parametric Function

Definition

A parametric function describes a set of equations that define coordinates as functions of an independent parameter (usually time). Instead of expressing y directly in terms of x, both x and y are expressed separately as functions with respect to another variable.

Related terms

Parameterization: Parameterization refers to finding equations that describe variables in terms of an independent parameter such as time. It allows us to represent complex curves or motions using simpler equations.

Eliminating the Parameter: Sometimes, we want to express a parametric function in terms of x and y directly, without the parameter. This process is called eliminating the parameter and involves solving for x and y in terms of the parameter.

Symmetry: Parametric functions can exhibit various types of symmetry, such as horizontal symmetry (reflection across the x-axis) or vertical symmetry (reflection across the y-axis). Analyzing symmetries helps understand the behavior of parametric curves.