Known information: A vector space V= C [-4,7] Subset S consists of functions of the form: e

Known information:

A vector space V= C [-4,7]

Subset S consists of functions of the form:  αe^bx (where a & b are real constants)

Question:

Determine if S is a subspace of V. I.e., does S satisfy the three conditions to be a subspace of V?

Conditions:

1) S contains the zero vector

2) S is closed under vector addition

3) S is closed under scalar multiplication