Vector-valued function
Okay kiddo, a vector-valued function is like a machine that takes in a number or a group of numbers and spits out a special type of number called a vector. A vector is like a special arrow with a direction and a length.
Let's say we have a machine that takes in one number and spits out a vector with two parts. We can call this machine f(x) and we'd write it like this:
f(x) = <x, x+1>.
If we put in the number 3 into this machine, we'd get the vector <3, 4>.
Now, what's really cool is that we can graph these vectors to see what they look like. We can draw them as arrows on a graph with a start point at the origin (0,0) and an end point at the coordinates given by the vector.
So for our example machine f(x), if we graphed all the vectors it spits out for all the possible input numbers, we'd see something that looks like a line going up and to the right.
And that's the basic idea of a vector-valued function! It's a way to turn numbers into vectors and see what they look like when we graph them.
Let's say we have a machine that takes in one number and spits out a vector with two parts. We can call this machine f(x) and we'd write it like this:
f(x) = <x, x+1>.
If we put in the number 3 into this machine, we'd get the vector <3, 4>.
Now, what's really cool is that we can graph these vectors to see what they look like. We can draw them as arrows on a graph with a start point at the origin (0,0) and an end point at the coordinates given by the vector.
So for our example machine f(x), if we graphed all the vectors it spits out for all the possible input numbers, we'd see something that looks like a line going up and to the right.
And that's the basic idea of a vector-valued function! It's a way to turn numbers into vectors and see what they look like when we graph them.
Related topics others have asked about: