Which function type includes a variable raised to the power of three?

A function that includes a variable raised to the power of three is categorized as a cubic function. In mathematics, cubic functions are defined by polynomial equations of the form ( f(x) = ax^3 + bx^2 + cx + d ), where ( a, b, c, ) and ( d ) are constants, and ( a ) is non-zero. The presence of the ( x^3 ) term is what characterizes the cubic nature of the function, which can exhibit unique properties such as inflection points and varying end behaviors depending on the sign of the leading coefficient.

In contrast, linear functions are represented by equations of the form ( f(x) = mx + b ) and have the highest exponent of 1, showing a straight line when graphed. Quadratic functions follow the form ( f(x) = ax^2 + bx + c ) with the highest exponent of 2, resulting in a parabolic shape. Exponential functions, on the other hand, are of the form ( f(x) = a b^x ) where the variable is in the exponent, distinctly different from polynomial functions. Therefore, the unique characteristic of cubic functions is identified through the presence of the variable