In earlier lessons, students interpreted and wrote statements in function notation to represent specific inputoutput pairs of a function (such as \(p(2.5)=18\)) or relationships between specific pairs (such as \(W(10)=W(12)\)).
In this lesson, students learn that function notation can also 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 \(f\) can be found by multiplying the input by 3 and then subtracting 10 from the result, we can write \(f(x) = 3x  10\) 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).
Lesson overview
 4.1 Warmup: Notice and Wonder: Two Functions (5 minutes)

4.2 Activity: Four Functions (10 minutes)
 Includes "Are you Ready for More?" extension problem
 4.3 Activity: Rules for Area and Perimeter (20 minutes)
 Lesson Synthesis
 4.4 Cooldown: Perimeter of a Square (5 minutes)
Learning goals:
 Create tables and graphs to represent a function given statements in function notation.
 Interpret rules of functions that are expressed using function notation.
 Use function notation to write equations that represent rules of functions.
Learning goals (student facing):
 Let’s look at some rules that describe functions and write some, too.
Learning targets (student facing):
 I can make sense of rules of functions when they are written in function notation, and create tables and graphs to represent the functions.
 I can write equations that represent the rules of functions.
Standards:
 This lesson builds on the standard: CCSS.8.F.A.1MS.8.F.1MO.8.F.A.1bMO.8.F.A.1cMO.8.F.A.1a
 This lesson builds towards the standard: CCSS.HSFBF.A.1MS.FBF.1MO.A1.LQE.A.3
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