In this lesson, students use rules of functions to find the output when the input is given (or to evaluate functions) and to find the input when the output is known (or to solve equations that define functions). They also interpret rules of functions in terms of a situation. Along the way, they practice reasoning quantitatively and abstractly (MP2).

The term linear function is introduced here. In middle school, students learned that a relationship between two quantities is linear if one quantity changes at a constant rate relative to the other. Students see that a linear function can be understood in similar terms: A function is linear if the output changes by a constant rate relative to its input.

This lesson includes an optional activity that is designed to enable students to use technology to graph and evaluate functions expressed in function notation. This skill can help to develop students’ understanding of functions and ability to solve problems in this unit and in future units.