Lesson 2

Function Notation

Lesson Narrative

This lesson introduces students to function notation. Students encounter situations in which referencing certain functions and their input-output pairs gets complicated, wordy, or unclear. This motivates a way to talk about functions that is more concise and precise.

Students learn that function notation is a succinct way to name a function and to specify its input and output. They interpret function notation in terms of the quantities in a situation and use function notation to represent simple statements about a function. The work in this lesson prompts students to reason quantitatively and abstractly (MP2) and communicate precisely (MP6).

Learning Goals

Teacher Facing

  • Interpret statements that use function notation and explain (orally and in writing) their meaning in terms of a situation.
  • Understand that function notation is a succinct way to name a function and specify its input and output.
  • Use function notation to express functions with specific inputs and outputs.

Student Facing

Let’s learn about a handy way to refer to and talk about a function.

Learning Targets

Student Facing

  • I can use function notation to express functions that have specific inputs and outputs.
  • I understand what function notation is and why it exists.
  • When given a statement written in function notation, I can explain what it means in terms of a situation.

CCSS Standards

Addressing

Building Towards

Glossary Entries

  • dependent variable

    A variable representing the output of a function.

    The equation \(y = 6-x\) defines \(y\) as a function of \(x\). The variable \(x\) is the independent variable, because you can choose any value for it. The variable \(y\) is called the dependent variable, because it depends on \(x\). Once you have chosen a value for \(x\), the value of \(y\) is determined. 

  • function

    A function takes inputs from one set and assigns them to outputs from another set, assigning exactly one output to each input.

  • function notation

    Function notation is a way of writing the outputs of a function that you have given a name to. If the function is named \(f\) and \(x\) is an input, then \(f(x)\) denotes the corresponding output.

  • independent variable

    A variable representing the input of a function.

    The equation \(y = 6-x\) defines \(y\) as a function of \(x\). The variable \(x\) is the independent variable, because you can choose any value for it. The variable \(y\) is called the dependent variable, because it depends on \(x\). Once you have chosen a value for \(x\), the value of \(y\) is determined.