Determine the family of curves represented by the equation y = ax^3 + bx.

Determine the family of curves represented by the equation y = ax^3 + bx.

Correct Answer: Cubic functions

Step 1: Identify the equation given, which is y = ax^3 + bx.
Step 2: Recognize that 'a' and 'b' are constants, meaning they do not change.
Step 3: Understand that 'x' is the variable that can change, affecting the value of 'y'.
Step 4: Note that the term 'ax^3' indicates that this is a cubic function because it has 'x' raised to the power of 3.
Step 5: Realize that changing the values of 'a' and 'b' will create different curves, but they will all be cubic functions.
Step 6: Conclude that the equation represents a family of curves, all of which are cubic functions with different shapes based on the values of 'a' and 'b'.

Cubic Functions – The equation represents a family of cubic functions characterized by the presence of the x^3 term, where the coefficients a and b determine the specific shape and position of the curves.