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Thread: Vector Valued Functions

  1. #1
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    Vector Valued Functions

    I dont understand what the second part of the question is asking for. My book only shows examples asking for a single functions such as r1(t) and not r2(t).

    In
    r2(t) can I let x = anything with a value of t in it? Such as x=(2-t) and then y would be y=Sqrt(2-t) ? I tried that but it was incorrect. Im stuck on this question. Any help would be appreciated.


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  2. #2
    MHF Contributor

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    Re: Vector Valued Functions

    ??? "$\displaystyle r_1$" and "$\displaystyle r_2$" are just two different functions. Whatever methods you learned or "$\displaystyle r_1$ work just as well for $\displaystyle r_2$! $\displaystyle r_2$ is completely separate from $\displaystyle r_1$ and has nothing to do with it.

    "$\displaystyle r_2(t)$" here is a linear function (its graph is a straight line) such that $\displaystyle r_2(0)= (1, 1)$ and [tex]r_2(1)= (0, 0). Notice that the (x, y) coordinates of the first point are the same, x= y= 1, and of the second point are the same, x= y= 0. Because this is a "linear function", that will always be true- that's why they have "y= x" after the boxes. Now, any linear function can be written as x= at+ b for numbers a and b. If x= 1 when t= 0 and x= 0 when t= 1, what must a and b equal?
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