Final answer:
The polynomial function f(x) = 3x^(2) + 2x + 1 is continuous on the interval [-2,2], as polynomials are continuous over their entire domain, which includes all real numbers.
Step-by-step explanation:
The question you've asked pertains to whether the function f(x) = 3x^(2) + 2x + 1 is continuous on the interval [-2,2]. Polynomials are continuous functions over their entire domain, which is all real numbers. Therefore, since this function is a polynomial, it is indeed continuous on the interval [-2,2] as well as on any other interval. To determine if a function is continuous, one can look for breaks, jumps, or vertical asymptotes in the function's graph; none of which are found in polynomial functions.
To be more technical, a function is continuous on an interval if it is continuous at every point within that interval. For a polynomial like f(x) = 3x^(2) + 2x + 1, which is comprised of terms consisting of real numbers, constants, and variables raised to whole number powers, continuity across any interval is guaranteed. Thus, in this particular case, f(x) does not have any points of discontinuity within the interval [-2,2].