Final answer:
In the vector valued function, 'b' represents an m-vector, a constant vector in m-dimensional space that's added to the vector resulting from the matrix-vector multiplication.
Step-by-step explanation:
In the given vector valued function f: Rn -> Rm expressed as, f(x) = A x + b, the term 'b' represents a constant vector that is added to the vector resulting from the matrix A multiplying the vector x. Since the function maps from n-dimensional space to m-dimensional space, the vector 'b' must be compatible with the m-dimensional space. Therefore, the answer is D) m-vector.
The constant vector 'b' does not change with different input vectors 'x' and is specifically added to each resultant vector after the transformation by the matrix A. It serves to translate the vector space as part of the linear transformation.
Considering vector operations, the addition of two vectors, like vector 'A' and vector 'b', results in a resultant vector. As suggested in the context of kinematics, if 'A' represents a displacement vector, adding 'b' would translate that displacement by the constant vector 'b', resulting in a new position.