Final answer:
The degree of the polynomial function f is likely 4, based on the symmetry and the rate of increase of f(x) values as x moves away from 0.
Step-by-step explanation:
The degree of a polynomial is the highest power of the variable in the polynomial. Examining the provided function, we notice that the values of f(x) change symmetrically as x moves away from 0 in both the positive and negative directions, which is typical of even degree polynomials. In particular, since the values of f(x) increase quite rapidly as x moves from -2 to -3 and from 2 to 3 (8 to 63 in both cases), we surmise that the polynomial has a relatively high degree. This quick increase suggests that the degree is at least 3. Moreover, because as x goes from -1 to -2 and from 1 to 2, f(x) goes from -1 to 8, which is an increase by 9 units, and from 2 to 3, it increases by 55 units (from 8 to 63), which indicates that the difference of differences is growing. This behavior is typical for fourth degree (quartic) functions, which suggests the degree of f is likely 4. This conclusion is supported by the fact that the set of points provided are symmetric around the y-axis and could be part of a polynomial function where f(x) = f(-x), which is a property of even functions, specifically, here, suggesting a quartic function.