For the given function 𝐫 of 𝑡 equals two 𝑡𝐢 plus two 𝑡 squared plus three 𝐣, evaluate 𝐫 of zero.
The function we’ve been given is a vector-valued function. It’s a function whose range is a vector or a set of vectors and whose domain is a subset of the real numbers. We’re looking to evaluate 𝐫 of zero. In other words, we’re going to let 𝑡 be equal to zero in our function 𝐫 of 𝑡. To find 𝐫 of zero, all we do is we replace 𝑡 with zero in our vector-valued function. So 𝐫 of zero is two times zero 𝐢 plus two times zero square plus three 𝐣. Two times zero is zero, and two time zero squared plus three is three. So we find that 𝐫 of zero is zero 𝐢 plus three 𝐣, which is simply three 𝐣.