# Quantities & Relationships

**This unit introduces the concepts of functions (how quantities relate to each other), and characteristics of functions.**

**1.1 Independent and Dependent Quantities**

**Explanation:**Notes | Annotated Notes

Khan video: Dependent & independent variables

**Practice Problems:**

**1.2 Modeling Relationships (define discrete or continuous)**

**Explanation:**Notes | Annotated Notes

Khan video: Dependent & independent variables: graphing

Khan video: End behavior of algebraic models

Khan video: Discrete and continuous random variables

Website Resource: Graphing Stories

**Practice Problems:**Khan exercise: End behavior of algebraic models

Desmos: Function Carnival (teacher use only)

Desmos Activity: Graphing Stories (teacher use only)

**1.3 Domain and Range**

**Explanations:**Notes| Annotated |Video: Youtube | SafeShare.tv

Khan video: Intervals and interval notation

Khan video: Worked example: domain and range from graph

Khan video: Worked example: determining domain word problem (real numbers)

Khan video: Worked example: determining domain word problem (positive integers)

Khan video: Worked example: determining domain word problem (all integers)

**Practice problems:**IXL: Q.2 Domain and range of relations (2CG) (discrete data only)

Khan exercise: Inequality from graph (on a number line; single inequality)

IXL: DD.3 Domain and range of absolute value functions: graphs (NV7)

IXL: FF.2 Domain and range of radical functions: graphs (UXG)

Desmos Activity: Domain and Range Introduction (uses compound inequalities) - teacher use only

Desmos Activity: Introduction to Domain and Range - teacher use only

Khan exercise: Domain and range from graph (uses compound inequalities)

Khan exercise: Function domain word problems (uses compound inequalities)

**1.4 Recognizing Functions**

**Explanations:**Khan video: What is a function? (optional)

Khan video: Recognizing functions from graph

Khan video: Does a vertical line represent a function?

Khan video: Recognizing functions from table

**Practice problems:**Desmos Acticity: Turtle Crossing (teacher use only)

Khan exercise: Recognize functions from graphs

Khan exercise: Recognize functions from tables

IXL: Algebra Q.4 Identify functions (from plotted points, list of points, table, mapping)

Worksheet #1

**1.5 Function Notation**

**Explanation:**Notes | Annotated

Khan video: Equations vs. functions

Khan video: Worked example: Evaluating functions from equation

Khan video: Worked example: matching an input to a function's output (equation)

Khan video: Worked example: evaluating functions from graph

Khan video: Worked example: matching an input to a function's output (graph)

Khan video: Function notation word problem: bank (honors)

Khan video: Function notation word problem: beach (honors)

**Practice problems:**Desmos activity: Carnival Functions, Part 2

Khan exercise: Evaluate functions

Khan exercise: Function inputs & outputs: equation

Khan exercise: Evaluate functions from their graph

Khan exercise: Function inputs & outputs: graph

Khan exercise: Function notation word problems (honors)

IXL: Algebra Q.6 Find values using function graphs (score of 90)

IXL: Algebra: Q.14 Interpret the graph of a function: word problems

IXL: Algebra: Q.15 Interpret functions using everyday language (U98)

**1.6 Functions: increasing, decreasing, and constant intervals; extrema **

**Explanation:**Khan video: Increasing, decreasing, positive or negative intervals (start the video at 2:34)

Khan video: Worked example: absolute and relative extrema

Khan video: Introduction to minimum and maximum points - uses more math symbols

Khan video: Graph interpretation word problem: basketball

**Practice problems****:**Desmos Activity: Increasing/Decreasing Functions (teacher use only)

Khan exercise: Increasing and decreasing intervals

Khan exercise: Relative maxima and minima

Khan exercise: Absolute maxima and minima

**1.7 Functions: positive and negative intervals and zeros**

**Explanation:**Notes | Annotated Notes

Khan video: Increasing, decreasing, positive or negative intervals (from 0:00 to 2:34)

Khan video: Worked example: positive & negative intervals

Khan video: Graph interpretation word problem: temperature

Khan video: Graph interpretation word problem: basketball

**Practice problems****:**Desmos Activity: Positive and Negative Intervals of a Function (teach use only)

Khan exercise: Positive and negative intervals

Khan exercise: Graph interpretation word problems

**Review**

**Adding Integers**

Explanation

Card game: war

Practice problems

Desmos Activity: Adding Integers (teacher use only)

**Subtracting Integers**

Explanation:

Desmos Activity:

In one day: Hot Air Balloon Model for Integer Operations (teacher use only)

In two days:

In three days:

Desmos Activity: Subtracting Integers

Practice problems

**Adding and Integers Integers**

Practice problems

ExamView Bank (purchase)

**Combing Like Terms**

Explanation:

Khan video: Intro to combining like terms

Practice problems:

Khan exercise: Combining like terms with negative coefficients

ExamView Bank (purchase)

**Multiplying and Dividing Integers**

Explanation

Practice problems

ExamView Bank (purchase)

**Mixed Review of All Operations with Integers**

Explanation

Practice problems

ExamView Bank (purchase)

**Order of operations**

Explanation:

Khan video: Evaluating expressions with two variables

Practice problems

Khan exercise: Evaluating expressions with one variable

Khan exercise: Evaluating expressions with multiple variables

ExamView Bank (purchase)