AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.9 Vector-Valued Functions
Notes
A vector-valued function $\vec p(t)=\langle x(t),y(t)\rangle$ gives the position of a moving point. It's another way to write a parametric function.
Practice
$\vec p(t)=\langle t^2,2t\rangle$. $\vec p(3)=$
Plug in $t=3$.
The distance from the origin of $\vec p(t)=\langle 3,4t\rangle$ at $t=1$:
$\displaystyle \sqrt{9+16}$.
A vector-valued function and a parametric function:
$\langle x(t),y(t)\rangle$ is the same as $x=x(t)$, $y=y(t)$.
Ready for more? Take the Unit 4 test.