If students are unsure how to set up and label the axes to graph the values of , consider saying:

• “Tell me how the labels for this graph compare to those of the axis for the graph of .”

• “How could the values for in the table help you set up the scale for the vertical axis?”

The purpose of this discussion is for students to understand that we can combine functions to make new functions and what that can mean for a specific context.

Invite students previously identified to share their explanations for the plot of , displaying their graphs for all to see to help students illustrate their ideas. Here are some questions for discussion:

• “What does mean in this context?” (In 2010 the average number of books bought per person in the US was about 8 books.)
• “Compare with . Describe how they are alike and how they are different.” (They both dip in 2011 and then go up, but then doesn't change much while appears to decrease. This is because the population is increasing while the number of books sold stays about the same, so the denominator is getting large while the numerator is about the same which means the quotient, , decreases.)
• “Let’s say is the average cost of a book, in dollars, in the US. What would the function defined by tell us?” (The average amount of money spent per person in the US on books in year .)

Conclude the discussion by asking students which graph they think is most useful for tracking book sales. After a brief quiet think time, invite students to share their reasoning. Depending on perspective, such as a local bookseller versus a large publishing company, both graphs can be useful for planning for future sales.

The purpose of this discussion is for students to share how they made their sketches, focusing on how the numerical value of the new function is defined by the sum of the numerical values of the two original functions. 

Invite previously selected students to share their approaches. Sequence the discussion of the approaches by the order listed in the Activity Narrative. If possible, record and display their work for all to see.

Next, invite previously identified students who took an incorrect approach to share in the order listed in the activity narrative. Where possible, identify what function the student did graph.

Connect the different responses to the learning goals by asking questions such as:

• “How did making a table before sketching change the accuracy of the graph?”
• “What patterns did you notice between the different graphs?”
• “What do you think a graph of E minus the other function would look like?”

If time allows, ask students to choose one of the questions and sketch the graph of a function defined by the difference between and the other function.