Final answer:
The function g(x) = 4x^2 - 6 is a quadratic function because it includes an x^2 term. This identifies it as part of the quadratic function family, having the form ax^2 + bx + c.
Step-by-step explanation:
The function g(x) = 4x2 - 6 belongs to the quadratic function family. Quadratic functions are characterized by the presence of an x2 term, which indicates that the highest power of x is 2. This form of the function is also known as a second-order polynomial. The standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants, and a is not equal to zero. In this case, g(x) has a term 4x2, which identifies it as a quadratic function, even though it does not have the bx or c terms explicitly written. This makes option (d) Quadratic the correct answer.