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# Algebra II

## Play and experiment with interactive graphs to build a strong foundation in algebra!

Use interactive graphing apps to explore and transform functions of all varieties: polynomials, exponents, logarithms, absolute value, and more. Learn a method of factoring not commonly taught in school, practice modeling scenarios, and do problem solving that reveals the beauty of mathematics.

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1. 1

### Introduction

Use experiments and play with graphs to learn algebra!

1. #### Modeling and Functions

Interact with functions by sliding their variables higher and lower to see what happens!

2. #### Transforming Functions

Practice predicting the behavior of function transformations.

3. #### Factoring and Beyond

Explore factoring polynomials from a new perspective, and learn a new factoring technique.

2. 2

### Function Fundamentals

Function notation, domain, range, and a plethora of graph types.

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#### Function Notation

Review the definition of "function" and the notation used to represent functions.

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#### Playing With Functions

Explore a variety of function types by experimenting and playing with their graphs.

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#### Domain and Range

Learn how the domains and ranges of functions depend on each other — and on the function types.

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3. 3

### Transformations

Move any function around or change its shape with a fixed set of rules.

1. Included with

#### Shifts and Stretches

How can a function wind up stretched and transposed up, down, left, or right on the plane?

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#### Symmetry

Throw some negatives into the mix and see what happens!

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#### Inverse Functions

What happens when the input becomes the output and the output becomes the input?

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#### Composition

First apply one function and then another, how does the initial input relate to the final output?

4. 4

Explore exponents and roots of all kinds.

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#### Powers

Explore a fast-growing power function used to model growth in finance and biology.

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#### Zero and Negative Exponents

What happens when the exponent is less than 1?

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#### Fractional Exponents

What happens when the exponent isn't an integer?

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This simplification technique lets you move and remove radicals.

5. 5

### Polynomials

Here you'll find every degree from zero to infinity.

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#### Playing With Polynomials

Get a feel for how polynomials work by interacting with their graphs.

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#### Polynomial Graph Basics

Solidify your understanding of how the graphs of polynomials are related to their functions.

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#### Polynomial Symmetries

Sometimes a bit of reflection can make things a lot easier.

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#### Projectile Motion

Apply quadratics to study and draw conclusions about these flying and falling objects!

6. 6

### Factoring Polynomials

Split polynomials down to their smallest parts!

1. Included with

#### Playing With Factored Form

Explore the art of factoring polynomials from new, graphical perspectives.

2. Included with

Master the techniques for quadratic factoring!

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#### More Factoring

Expand your factoring skills to cover cases where the leading coefficient is greater than 1.

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Apply one of the most famous formulas in early mathematics to factor some polynomials.

7. 7

### Rational Functions

Put together two polynomials with division, and a new world opens up.

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#### Direct and Inverse Variation

When one variable goes up, does the other go up with it?

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#### Direct and Inverse Variation With Powers

Explore what variation looks like when larger powers are involved.

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#### Asymptotic Behavior Part 1

Get closer and closer and closer... to infinity.

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#### Asymptotic Behavior Part 2

Learn how to tackle these tricky horizontal and slant asymptote cases!

8. 8

### Piecewise Functions

Make new functions by mashing together old ones.

1. Included with

#### Absolute Value Introduction

What are absolute value functions and how does arithmetic interact with them?

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#### Modeling Absolute Value Scenarios

Consider some real-life scenarios where the concept of absolute value applies.

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