AP®︎ Precalculus: Topic 4.1 Practice Test

Essential Knowledge: 4.1.A.1

A parametric function in $\mathbb{R}^{2}$, the set of all ordered pairs of two real numbers, consists of a set of two parametric equations in which two dependent variables, $x$ and $y$, are dependent on a single independent variable, $t$, called the parameter.

Essential Knowledge: 4.1.A.2

Because variables $x$ and $y$ are dependent on the independent variable, $t$, the coordinates $(x_i, y_i)$ at time $t_i$ can be written as functions of $t$ and can be expressed as the single parametric function $f(t) = (x(t), y(t))$, where in this case $x$ and $y$ are names of two functions.

Essential Knowledge: 4.1.A.3

A numerical table of values can be generated for the parametric function $f(t) = (x(t), y(t))$ by evaluating $x_i$ and $y_i$ at several values of $t_i$ within the domain.

Essential Knowledge: 4.1.A.4

A graph of a parametric function can be sketched by connecting several points from the numerical table of values in order of increasing value of $t$.

Essential Knowledge: 4.1.A.5

The domain of the parametric function $f$ is often restricted, which results in start and end points on the graph of $f$.