Unit 3

Functions

Understand what a function is, use function notation, identify domain and range, explore linear functions and slope, graph linear equations, write equations in slope-intercept and standard form, identify parallel and perpendicular lines, write linear functions from multiple representations, compare functions, and connect arithmetic sequences to linear functions.

Unit 3 · 14 pages

Chapters

00Cover

Cover

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 3 Functions.

3.1

Introduction to Functions

Understand the definition of a function, identify functions from tables, graphs, and mappings using the vertical line test.

3.2

Function Notation

Read and write function notation f(x). Evaluate functions for given input values and interpret outputs in context.

3.3

Domain and Range

Identify the domain (inputs) and range (outputs) of a function from tables, graphs, and equations.

3.4

Linear Functions

Graph linear functions using slope and y-intercept. Write equations in slope-intercept form y = mx + b.

3.5

Rate of Change & Slope

Calculate slope as rate of change between two points. Interpret positive, negative, zero, and undefined slopes.

3.6

Graphing Linear Equations

Graph linear equations using tables of values, intercepts, and slope-intercept method.

3.7

Slope-Intercept Form

Write and graph linear equations in slope-intercept form y = mx + b.

3.8

Standard Form of Linear Equations

Write linear equations in standard form Ax + By = C and convert between forms.

3.9

Parallel and Perpendicular Lines

Identify and write equations of parallel and perpendicular lines using slope relationships.

3.10

Writing Linear Functions from Multiple Representations

Write linear functions from tables, graphs, two points, and verbal descriptions by identifying slope and initial value.

3.11

Comparing Functions

Compare functions shown in different representations — equations, tables, graphs, and verbal descriptions — by analyzing rate of change and initial value.

3.12

Arithmetic Sequences as Linear Functions

Identify arithmetic sequences, find the common difference, and write explicit and recursive rules. Connect the common difference to slope.

3.13

Unit Review

Comprehensive review of all Unit 3 topics: functions, notation, domain and range, linear functions, rate of change, graphing, slope-intercept form, standard form, parallel and perpendicular lines, writing functions, comparing functions, and arithmetic sequences.

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