About This Chapter
Graph Symmetry - Chapter Summary and Learning Objectives
In math, the term symmetry refers to the identical shapes found on either side of a line or plane, as well as the numerical relationships in an equation or a function. Although symmetry is typically associated with geometry, the expression can also be applied to the mathematical graphs used in algebra and calculus. For example, you might use a graph to depict a quadratic equation and diagram a parabola, or the curve of an open plane. In calculus, a graph can be used to determine if a mathematical function is even or odd.
In this chapter, the instructor will use easy-to-follow illustrations and language to help you understand the graphing concepts found in an advanced high school algebra or precalculus course. After you've finished watching the tutorials and taking the online self-assessment quizzes, you should be able to identify and illustrate symmetry:
- About the x-axis and y-axis on a graph
- About the origin on a graph
- Within odd and even functions
|Recognizing Symmetry Graphically, Algebraically and Numerically about the X-axis and Y-axis||Detect symmetry graphically, numerically and algebraically.|
|Recognizing Symmetry Graphically, Algebraically and Numerically about the Origin||Detect symmetry graphically, numerically and algebraically.|
|Even and Odd Functions||Define even and odd functions algebraically. Identify even and odd functions graphically.|
1. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis
When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.
2. Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin
If you look at flowers and fruits, you'll see that many of these items in nature are symmetrical. In this lesson, learn about symmetry about the origin of a graph. When you are finished, test your knowledge with a short quiz!
3. Identifying the Line of Symmetry: Definition & Examples
Symmetry can occur in many different ways in mathematics. In this lesson, learn how to identify unique forms of symmetry by finding the line of symmetry.
4. Even & Odd Functions: Definition & Examples
Even and odd functions are an aspect of line symmetry. You can use knowledge of even and odd functions to quickly identify equation symmetry. After this lesson, test your knowledge with a short quiz!
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Other chapters within the Math 105: Precalculus Algebra course
- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105