
## Section5.3*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.

### Subsection5.3.1Parameterizing of the graph of a function, $y=f(x)$

From left-to-right:

From right-to-left:

### Subsection5.3.3Synchronized Space Curves

Piecewise-defined vector-valued functions:

Synchronizing motion along multiple curves at the same time: