A: The function is decreasing at a decreasing rate (that is, the changes are negative and growing in size), B: The function is decreasing at a constant rate. C: The function is decreasing at an increasing rate (that is, the changes are negative but becoming smaller in size). D: The function is increasing at a decreasing rate (that is, the changes are positive but shrinking), E: The function is increasing at a constant rate. F: The function is increasing at an increasing rate.

Did you know that many mathematical functions can be described as either linear or nonlinear? In a linear function, the rate of change remains constant, much like riding a smooth escalator. Meanwhile, nonlinear functions can take you on a more twisty, turny ride, creating fascinating curves and variations in their slopes. This distinction can help you understand everything from economics to physics! In real-world scenarios, many phenomena can be modeled using these types of functions. For instance, when examining the growth of a company's revenue, you may find it increasing at an increasing rate if market conditions are favorable, resembling a rocket launch! Conversely, a product nearing the end of its life cycle might show a decreasing rate of revenue, indicating a gradual decline. Understanding these patterns can greatly aid in effective business forecasting and decision-making.