Lesson 1: Relations and Functions

What is the definition of a function?
How do we verify that a set of ordered pairs is a function?
When you are looking at a graph, how do you know if it is a function?

Ordered pair; Relation; Function; Independent; Dependent

MBA 3A. Explain the concept of a function and use function notation.

Lesson Description
This lesson defines the fundamental relationship between two sets of data. Students will learn to distinguish between a general relation and a specific function. Key topics include:

Definitions: Understanding a relation as a set of ordered pairs and a function as a special relation where each input has exactly one output.

Domain and Range: Identifying the set of all possible input values (Domain) and all possible output values (Range) from lists, tables, and graphs.

Visual Testing: Using the Vertical Line Test to determine if a graph represents a function.

Mapping Diagrams: Using arrows to visualize how elements of the domain connect to elements of the range.

Purpose
The purpose of Section 7.1 is to establish a logical framework for predictability. In mathematics and science, we look for functions because they provide a "guarantee"—if you know the input, the output is certain. By identifying the domain and range, students learn to define the boundaries of a problem (e.g., "Time cannot be negative"). This conceptual shift is the gateway to all higher-level math, including College Algebra, Precalculus, and beyond, where the study of functions becomes the primary focus.

Depth of Knowledge (DOK) Level
DOK Level 1 & 2

Level 1 (Recall & Reproduction): Defining domain and range, identifying ordered pairs, and stating the definition of a function.

Level 2 (Skill/Concept): Categorizing relations as functions or non-functions. Students must apply the Vertical Line Test to various graphs and translate between different representations of relations (e.g., turning a table of values into a mapping diagram or a set of ordered pairs).

The distance a car travels from when the brakes are applied to the car's complete stop is the stopping distance. This includes time for the driver to react. The faster a car is traveling the longer the stopping distance. The stopping distance is a function of the speed of the car.

Class and online work

Use practice problems 1-4, page 167 to assess students' understanding of the lesson concepts