# Lesson 1

Describing and Graphing Situations

### Lesson Narrative

In this opening lesson, students recall the meaning of functions (which was introduced in grade 8) and encounter examples of functions and their representations in context.

Students consider why certain relationships could be seen as functions while others could not be. By analyzing tables and graphs that represent both functions and non-functions, and by interpreting descriptions of each situation, students are reminded that a function assigns exactly one output value to each input. If an input could have more than one possible output, then the relationship cannot be a function.

As they analyze and sketch graphs of functions, students are also reminded that each point on a graph represents an input-output pair of the function. They interpret coordinates on a graph of a function in terms of the quantities in the situation represented.

Students practice making sense of problems and persevering in solving them (MP1) as they look for and explain correspondences between verbal descriptions, tables, and graphs. They engage in aspects of modeling (MP4) as they identify input and output variables in real-life situations and create representations of their relationships.

The work here prepares students to describe and talk about functions more formally in upcoming lessons.

### Learning Goals

Teacher Facing

• Interpret descriptions and graphs of functions in context.
• Understand that a relationship between two quantities is a function if there is only one possible output for each input.
• Use words and graphs to represent relationships that are functions, including identifying the independent and dependent variables.

### Student Facing

Let’s look at some fun functions around us and try to describe them!

### Student Facing

• I can explain when a relationship between two quantities is a function.
• I can identify independent and dependent variables in a function, and use words and graphs to represent the function.
• I can make sense of descriptions and graphs of functions and explain what they tell us about situations.

Building On

### 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.

• 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.