In this lesson, students learn that, in addition to individual input-output pairs, function notation can be used to describe the rule of a function or how a function behaves generally, at any value of input. For instance, they see that if the output of a function can be found by multiplying the input by 3 and then subtracting 10 from the result, we can write to represent this rule. We can also use this rule (either the verbal description or the equation) to find the output for any input. In some cases, the rule can also be used to find the input when we know the output.

Students continue to decontextualize given situations into symbolic representations and to contextualize the latter in order to solve problems (MP2). To connect different representations of functions defined by rules, they look for and make use of structure (MP7).