Multifunction/Examples

Examples of Multifunctions

Arbitrary Multifunction

Consider the implicit function:

$y^2 = x + 2$

For $x > 2$, there are $2$ values of $y$ for every $x$.

Hence on that domain $y$ is a two-valued (multi)function of $x$.

Unit Circle

Consider the equation for the unit circle whose center is at the origin of the Cartesian plane:

$x^2 + y^2 = 1$

This can be considered as the graph of a multifunction whose domain is the closed real interval $\closedint {-1} 1$ and whose branches are:

\(\ds y\)

\(=\)

\(\ds +\sqrt {1 - x^2}\)

\(\ds y\)

\(=\)

\(\ds -\sqrt {1 - x^2}\)