Invite students to share some suggestions for a graphing window that are more helpful and those that are less helpful. Ask them to explain their reasoning.

Help students understand that, as a general rule, the $x$ values to show for a graph are usually determined by the quantity we are interested in studying. The $y$ values need to be selected carefully so that:

• Data of interest shows up on the graph.
• Interesting trends (of increase or decrease) are as visible as possible.

If time permits, discuss:

• “Why does the graph show such a sharp decrease between $x$ values of 0 and 2 and then start to flatten out?” (The decay factor is 0.2, which means that whenever $x$ increases by 1, it loses 0.8 of its quantity and keeps only 0.2. That decay is more apparent when the quantity is larger. As it gets smaller, and given the scale of the graph, it is harder to see the change. For example, when $x$ increases from 0 to 1, $f(x)$ decreases by 320, because $(0.8) \boldcdot 400=320$. But when $x$ increases from 2 to 3, $f(x)$ decreases by $(0.8) \boldcdot 16$ (or 10.8), which is a much smaller drop.)