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Section 5.3 *Vector-Valued Functions

Vector-valued functions allow us to represent a set of parametric equations defining a curve in the \(xy\)-plane or in space as a single function of time. The outputs of vector-valued functions are vectors, as their name clearly indicates. The vector output can be said to point to the location of a particle that is traveling along the curve it defines.

Subsection 5.3.1 Parameterizing of the graph of a function, \(y=f(x)\)

From left-to-right:

From right-to-left:

Subsection 5.3.2 Various Parameterizations of a path

Subsection 5.3.3 Synchronized Space Curves

Piecewise-defined vector-valued functions:

Synchronizing motion along multiple curves at the same time: