Unit 3 — Functions

Unit 3 · Functions

Functions

Understand what a function is, use function notation, identify domain and range, explore linear functions and slope, write linear functions from multiple representations, compare functions, and connect arithmetic sequences to linear functions.

Estimated Time

30–40 minutes

Difficulty

Easy

13 Lessons
13 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 3 — Functions introduces one of the most important ideas in mathematics. You will learn what makes a relation a function, use function notation, identify domain and range, and explore linear functions, slope, and rate of change through graphs and real-world contexts.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Define a function and identify functions from tables, graphs, and mapping diagrams.
Goal 2Use the vertical line test to determine whether a graph represents a function.
Goal 3Read and write function notation f(x) and evaluate functions for given input values.
Goal 4Identify the domain (inputs) and range (outputs) of a function.
Goal 5Graph linear functions using slope and y-intercept in slope-intercept form y = mx + b.
Goal 6Calculate slope as rate of change between two points and interpret its meaning in context.

Skills You Will Master

Identifying functions
Function notation f(x)
Domain & range
Graphing linear functions
Slope & rate of change
Real-world applications

Real-World Connection

Functions are everywhere. When a streaming service recommends a show based on your watch history, it is using a function. When a GPS calculates your arrival time based on distance and speed, that is a function. Businesses use functions to model revenue, scientists use them to track population growth, and engineers use them to design bridges. Understanding functions — and especially linear functions — gives you the mathematical lens to describe, predict, and analyze the world around you.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter