We all know that some set of scalar functions $f$ can be in a vector space, for example a Hilbert space, or some finite-dimensional space like the vector space of all polynomials whose degree is $\leq n$. And, alongside this, is very common to hear the phrase "All vectors are tensors of rank 1".
This would made possible for one to infer: "All functions that belong to some vector space $V$ are vectors and hence are tensors". But the idea of a scalar function or a polynomial being a tensor isn't very much clear to me, since we know that vectors must hold specific rules of transformation under a coordinate change.
What am i missing?