5. For the function , which of the following describes the transformations that have occurred?

To understand the transformations of the function , you can break it down into parts. First, the coefficient in front of indicates a vertical stretch by a factor of . This means that the graph of will be stretched vertically, making it rise more steeply as it moves away from the origin.

Next, the term suggests a vertical shift downward by units. So, to visualize this, take the stretched graph of and move every point down by units. In summary, the function undergoes a vertical stretch and a downward shift, resulting in a more pronounced, steeper curve that sits lower on the graph.

Now, let’s add a little context! The base cubic function is famous for its distinctive “S” shape, rising to the right and falling to the left through the origin. When you apply these transformations to it, you not only enhance its steepness with the vertical stretch but also reposition it in the coordinate plane, making it a fun exercise in observing how algebraic manipulation changes the visual representation of a function!