If you had a computer that could track the number of cereal boxes on the shelf of a market continuously over a 1-week period would you expect the graph of the number of boxes on the shelf versus time to be a continuous (unbroken) curve? Explain your reasoning.

I think the answer could be no, if the cereal product were purchased until the shelf were empty. Then there would be a break in the graph. However, it could be yes if the product were never purchased so much as to empty the shelf.

Am I on the right track?

The number of boxes goes throguh a number of discontinuous "steps" whenever a box is added or bought. That makes the function discontinuous.

Yes, you are on the right track. It is possible for the graph of the number of cereal boxes on the shelf versus time to either be continuous or have breaks, depending on the purchasing behavior and stock replenishment.

If the cereal product is consistently restocked on the shelf before it is completely sold out, then the graph would appear as a continuous (unbroken) curve. In this case, the number of cereal boxes would gradually decrease as customers purchase them, and then increase again each time new boxes are added to the shelf.

However, if the cereal product is repeatedly purchased until the shelf is completely emptied, there would be a break in the graph. Initially, the graph would show a gradual decrease in the number of boxes until all the boxes are sold. At that point, the graph would have a break, indicating that the shelf is empty. The graph would only continue once new boxes are restocked on the shelf.

So, in summary, whether the graph of the number of boxes on the shelf versus time is continuous or has breaks depends on the purchasing behavior and stock replenishment of the cereal product.