Final answer:
The function f(x) = 2x^2 + 7x + 6 is a polynomial function without a hole because it does not have a denominator with a factor that could be canceled out, causing a removable discontinuity.
Step-by-step explanation:
In the context of function graphs, a hole is a point where the function is not defined, which occurs when a factor is both in the numerator and the denominator of a rational function, after simplifying. However, the quadratic function given, f(x) = 2x^2 + 7x + 6, is a polynomial function and does not have denominators that produce removable discontinuities (holes). Thus, since there are no factors in the denominator that can be cancelled out with the numerator, the correct answer to the question is C) No hole.