About This Chapter
Graphing and Rational Equations - Chapter Summary and Learning Objectives
Rational equations can have fractions with x's in the denominators, numerators or both. In these lessons, instructors explain how to find the least common denominator towards solving these types of equations. Once you've found the least common denominator, you can learn how to multiply the whole number by that denominator to get rid of all the fractions. Using your previously learned algebra skills, you can then solve the problem.
Mathematical reflections are just 'flips' of objects across lines of reflection where the shape and size aren't changed. In this lesson, you can practice starting at the origin and move on the coordinate plane according to the slope and shift of the equation to find the graph that's 'reflected' on the other side of the x-axis. This chapter can help you understand the following:
- Concept of mathematical reflections
- Graphing essentials, including origin, x-axis and y-axis
- Steps for graphing reflections
- Methods for finding the least common denominator
- Steps for solving rational equations after finding the least common denominator
|How to Graph Reflections Across Axes, the Origin, and Line Y=X||Examine the elements of graphs. Learn what mathematical reflections are and how to graph them using y-axis, x-axis, origin and the line y=x.|
|Solving Rational Equations and Finding the Least Common Denominator||Review how to find the least common denominator for fractions. Find out how to multiply and solve rational equations after you determine the least common denominator.|
1. How to Graph Reflections Across Axes, the Origin, and Line y=x
A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.
2. Solving Rational Equations and Finding the Least Common Denominator
When solving rational equations, just like with any other fractions, you must first find the least common denominator. This lesson will show you how to find the least common denominator and also solve the rational equations.
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Other chapters within the Math 103: Precalculus course
- Evaluating Exponential and Logarithmic Functions
- Foundations of Linear Equations
- Factoring and Graphing Quadratic Equations
- Exponents and Polynomials
- Piecewise and Composite Functions
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Studying for Math 103