Final answer:
To determine if a function is surjective, you must verify whether every element in the codomain is the image of at least one element in the domain. Surjectivity is not determined by whether a function is odd, one-to-one, or has no critical points.
Step-by-step explanation:
To check if a function is surjective, or onto, we determine if every element in the codomain is mapped to by some element in the domain. This is represented by option A. Therefore, for a function to be surjective, for every y in the codomain, there must exist an x in the domain such that f(x) = y. This does not necessarily have anything to do with critical points (option B), whether the function is odd (option C), or if the function is one-to-one (option D, which relates to injectivity, not surjectivity).
The explanation of surjectivity is not directly related to the property of an odd function, which states that the integral of an odd function over a symmetric interval (e.g., from -a to a) will be zero. This is due to the fact that the function has symmetry about the origin, and areas above and below the x-axis cancel out. Therefore, while odd functions have interesting attributes and are useful in many areas of mathematics, their properties do not define surjectivity.