# 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.

### 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.

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.