# Lesson 3

Interpreting & Using Function Notation

### Lesson Narrative

In this lesson, students continue to develop their ability to interpret statements in function notation in terms of a situation, including reasoning about inequalities such as $$f(a) > f(b)$$. They now have to pay closer attention to the units in which the quantities are measured to effectively interpret symbolic statements. Along the way, students practice reasoning quantitatively and abstractly (MP2) and attending to precision (MP6).

Students also begin to connect statements in function notation to graphs of functions. They see each input-output pair of a function $$f$$ as a point with coordinates $$(x, f(x))$$ when $$x$$ is the input, and use information in function notation to sketch a possible graph of a function.

Students’ work with graphs is expected to be informal here. In a later lesson, students will focus on identifying features of graphs more formally.

### Learning Goals

Teacher Facing

• Describe connections between statements that use function notation and a graph of the function.
• Practice interpreting statements that use function notation and explaining (orally and in writing) their meaning in terms of a situation.
• Sketch a graph of a function given statements in function notation.

### Student Facing

Let’s use function notation to talk about functions.

### Student Facing

• I can describe the connections between a statement in function notation and the graph of the function.
• I can use function notation to efficiently represent a relationship between two quantities in a situation.
• I can use statements in function notation to sketch a graph of a function.

### 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.