About This Chapter
Absolute Value Equations - Chapter Summary and Learning Objectives
Let instructors teaching this chapter show you how absolute value can be used to represent a number's magnitude. Through a combination of entertaining video lessons and quizzes, you can also learn what to do when you see absolute value notation in an equation and get tips for performing translations, dilations and reflections to change the location or shape of an absolute value's graph. By the end of this chapter, you should be able to do the following:
- Evaluate absolute value expressions
- Solve and graph absolute value equations
- Transform an absolute value's graph
|What Is an Absolute Value?||Explore the uses of absolute value and familiarize yourself with absolute value notation. Examine methods for solving equations that include these types of expressions.|
|How to Evaluate Absolute Value Expressions||Learn how to evaluate absolute value expressions by substituting numbers for variables.|
|How to Solve an Absolute Value Equation||Find out how to split absolute value equations in two and solve for x.|
|Solving Absolute Value Practice Problems||Practice the steps involved in solving absolute value equations.|
|How to Graph an Absolute Value and Do Transformations||Identify components of an absolute value's graph. Discover methods for performing translations that shift graphs to the left and right or up and down.|
|Graphing Absolute Value Equations: Dilations and Reflections||Understand how to perform dilations and reflections used to stretch or shrink an absolute value's graph.|
1. What is an Absolute Value?
When we're talking and comparing numbers, we often don't care whether its positive or negative, just how big it is. This is often called the magnitude of a number and we find it by taking the absolute value. Learn all about it here!
2. How to Evaluate Absolute Value Expressions
Substituting values into absolute values doesn't have to be too hard, but it can be if you're given deceiving beginning information. See if you're up to it by checking out this video!
3. How to Solve an Absolute Value Equation
Once you get familiar with any new operation, the next step in any algebra class is to learn how to solve equations with that operation in them. Absolute values are no different. Solve absolute value equations here!
4. Solving Absolute Value Practice Problems
There are many easy mistakes to make when solving absolute value equations. Learn how to avoid those mistakes here by working on examples of absolute value equations with operations on the inside and the outside of the absolute value.
5. How to Graph an Absolute Value and Do Transformations
Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. As well as teaching you how to graph absolute values, this video will focus on a specific group of transformations called translations. Learn all about what that means here!
6. Graphing Absolute Value Equations: Dilations & Reflections
Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing! In this lesson, you'll practice different transformations of absolute value graphs.
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Other chapters within the Precalculus: High School course
- Working With Inequalities
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations