Which of the following is the correct representation of a cubic function?

The representation of a cubic function is characterized by the presence of a term containing the variable raised to the third power. In the context of the given choices, the correct representation is indeed the option that includes ( ax^3 ).

A cubic function typically is expressed in the form ( y = ax^3 + bx^2 + cx + d ), where ( a, b, c, ) and ( d ) are constants and ( a ) is not equal to zero. This format allows for various behaviors, including having one, two, or three real roots, and it can represent a wide variety of shapes when graphed.

In the specific option identified as correct, ( y = ax^3 + c ), the function includes the cubic term ( ax^3 ) and an additional constant ( c ), which is enough to qualify it as a cubic function. This form indicates that the function's highest degree term is to the third power, signifying that it is indeed cubic.

The other options fail to represent a cubic function because they do not include a term with the variable raised to the third power. For instance, the first choice represents a quadratic function with the highest degree of 2, the third choice is