How to make a vector function from a f(x) function

[DrummingAtom]

Let's say I want to turn f(x) = x² into a vector function. How would I do that?

I know I can take plots of f(x) = x² then plug them into the Pythagorean theorem to get the distance from the origin and then I would also know the direction. But is that doesn't seem the same as a vector valued function.

 

[gb7nash]

Let's say I want to turn f(x) = x² into a vector function. How would I do that?

I'm not sure what you mean by this. Do you just want a vector that represents the x and y values wrt the origin? If so, all you need is:

<x,f(x)> = < x , x² >

 

[DrummingAtom]

Wouldn't the length be needed for a vector function? The whole "magnitude and direction" thing for vectors. Something like V=(direction, length).

 

[gb7nash]

Wouldn't the length be needed for a vector function? The whole "magnitude and direction" thing for vectors. Something like V=(direction, length).

For any vector <x,y>, you can find the length by \sqrt{x^2 + y^2}.

In this case, if you want the length from the origin to a point (x,f(x)), all you need is \sqrt{(x)^2+(x^2)^2}

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Just out of curiousity, what are you trying to do with this?

 

[DrummingAtom]

Ok, I came up with this too: \sqrt{(x)^2+(x^2)^2}.

I guess I just wanted to figure out if the vector function would be in terms of (direction, length) or only the position. Thanks for help.

 

[HallsofIvy]

It sounds to me like you have some function f(x) and want to construct a vector that represents the postion vector of (x, f(x)).

The position vector of any point (x, y) is xi+ yj so the position vector of (x, f(x)) is xi+ f(x)j.