# Vector Valued Functions

• Sep 13th 2013, 06:35 AM
petenice
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.

Attachment 29166
• Sep 13th 2013, 07:40 AM
HallsofIvy
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?