Final answer:
A function passing through the origin does not necessarily have an even degree; it could be even or odd. This statement is false because a function's degree is not determined by whether it passes through the origin.
Step-by-step explanation:
The question "If the function passes through the origin, does that mean it has an even degree?" is a mathematical inquiry related to the characteristics of polynomial functions. The truth of this statement can be false. A function passing through the origin means that the origin (0,0) is a point on the function, which implies that the function has a root at x = 0. However, this does not necessarily indicate whether the function has an even or odd degree. Polynomials can have any degree and still pass through the origin. For instance, the polynomial f(x) = x^3 passes through the origin and has an odd degree, while the polynomial g(x) = x^2 also passes through the origin but has an even degree. Therefore, whether a function of the even degree can entirely depend on its specific form rather than simply whether it passes through the origin.