Every function we have studied so far has had one input and one output. Usually our variable for the input is [math]x[/math] and our variable for the output is [math]y[/math]. To indicate that our output variable is [i]dependent[/i] on our choice of input variable we write [math]y=f\left(x\right)[/math], literally read "[math]y[/math] is a function of [math]x[/math]".[br][br]In this unit we will introduce a new type of function, one that has one input, usually named [math]t[/math] and two outputs, usually named [math]x[/math] and [math]y[/math]. Our two output variables are [i]dependent [/i]on our choice of input variable. We will often write [math]x\left(t\right)[/math] and [math]y\left(t\right)[/math] indicating that [math]x[/math] and [math]y[/math] are each functions of [math]t[/math]. Later when you take my Multivariable Calculus class I will teach you to write [math]c\left(t\right)=\left(x\left(t\right),y\left(t\right)\right)[/math] indicating that the function [math]c[/math] inputs a single number [math]t[/math] and outputs a two-dimensional point [math]\left(x\left(t\right),y\left(t\right)\right)[/math].[br][br]We refer to the functions [math]x\left(t\right)[/math] and [math]y\left(t\right)[/math] as [b][color=#ff0000]parametric equations[/color][/b], and the variable [math]t[/math] is called the [b][color=#ff0000]parameter[/color][/b]. In the GeoGebra file below you can practice plotting the output of such a function by plugging in various values for the parameter.