The mathematical purpose of this lesson is for students to recall the definition of a function and how to represent functions. In the warm-up, students investigate an example where a relationship is a function for one choice of independent and dependent variable, but not for the other choice. Then, they examine several examples of functions and non-functions from the perspective of “Can we figure out . . . ?” Then, they decide which of the functions can be represented by a given expression.
When deciding how a situation can be represented symbolically, students are practicing decontextualizing (MP2). This work continues in the final activity, where students match representations of four different functions. They are required to explain how they know they have found a match, which is an example of constructing viable arguments (MP3) and involves attending to precision with the language they use to describe the features of the representations (MP6).
The work of this lesson connects to previous work done in grade 8 when students learned what a function is, and it connects to work done in an earlier unit when students learned to represent functions using function notation and written descriptions. This lesson prepares students to extend the definition of a function and how to represent exponential functions in the associated Algebra 1 lesson.
- Review representations of functions and notation.
- Let’s represent functions.