Lesson 6.5 Linear Equations & Functions

# Functions

#### Materials

• CCB Mathematics pages 200 - 205

#### Standards

• Define, evaluate, and compare functions.

• Use functions to model relationships between quantities.

#### Objectives

• Identify a function

• Determine whether an equation represents a function

#### Key Concept

• You can look at a function as a set of instructions that tells you what to do with the input, or values you put in. The result of the instructions is called the output. Functions are equations that provide only one output for each input.

#### Vocabulary

Tier 2 FunctionInputOutput Linear FunctionNonlinear FunctionVertical Text

## Before Lesson

In this lesson, students develop their understanding of the concept of a function. To determine student readiness, write examples of simple equations, such as 2x=18, on the board and ask students to solve for the variable. Ask students to work in pairs to generate more simple equations, exchange problems with their partners, and solve for the variables. Observe students as they work, intervening if necessary.

## Background

A function has both an input and an output. A function can be viewed as a set of instructions in which an input value makes it possible to calculate an output value. Functions can be either linear or nonlinear. The vertical line test can be used to determine whether a graph represents a function. Have students graph capital letters of the alphabet to see if any of the letters can be thought of as functions (only V and Ware, possibly M depending on how it is drawn).

## Guided Practice

• What Is a Function?
• Is It a Function?
• Function Categories
• Perimeter of a Square
• Area of a Square

## Core Skill

Build Lines of Reasoning: To reinforce the concept of a function as a set of instructions, have students read the text and think through the process of writing instructions for the function that converts temperature from Fahrenheit to Celsius. Next, have students share their instructions and explain their thinking. Discuss students’ solutions as a class, ask relevant questions, and form a consensus about the best instructions. Have students test the instructions for accuracy.

Interpret Graphs and Functions: Ask students to read the text and summarize the value of examining the form of a function, that is, whether it is represented by y=mx+b, to determine whether a function is linear or nonlinear.

## Extension

Picture Dictionary: Review Ask students to show and explain the picture dictionary entries they created before the lesson. As students talk about their entries, prompt them to discuss what revisions they might want to make to better explain the words the pictures represent now that they have learned more about functions.

Interpret Information from a Complex Graph: Have students research and find graphical representations of exponential functions. Have students use two-column charts to calculate data points and then plot the data points on a graph.