When the function values are the same for every value of x, many students become confident that the rules are equivalent. However, there are numerous students who need to evaluate each expression for one or more values of x before they are convinced. The function values can be compared and the process can be repeated for other values of x, if needed. Another topic related to this lesson is discrete versus continuous functions. Students may debate how the company charges the customer.
Some companies charge by the minute and others by increments of minutes.
These questions, while unanswered by the advertisement, provide a springboard for a discussion of discrete and continuous functions. Students at this level often have only dealt with continuous functions for which the coordinates are all connected. For discrete functions there is no such connected graph because there are no function values between the plotted coordinates. Students need numerous experiences in rich problem-solving contexts to foster algebraic thinking. Further, they need to become comfortable with various forms of representation both to interpret data and also to compare it in different forms.