Final answer:
The function f(n) = (n-1)^2 + 3n is a quadratic function because, after expanding, it simplifies to a second-order polynomial of the form an^2 + bn + c.
Step-by-step explanation:
If f(n) = (n-1)^2 + 3n, we need to determine whether the function is linear, quadratic, exponential, or cubic. By expanding the equation, we get f(n) = n^2 - 2n + 1 + 3n, which simplifies to f(n) = n^2 + 1n + 1. This equation is of the form an^2 + bn + c, where 'a', 'b', and 'c' are constants. Since the highest power of the variable n is 2, the function is a quadratic function. Therefore, the correct answer is b) The function is quadratic.