Rational Functions
Lessons in this chapter
About Rational Functions
Rational Functions covers graphing functions built from fractions, plus every algebraic operation and equation involving them.
Inverse Variation introduces the simplest rational relationship, where one quantity varies inversely with another, before Graphing Rational Functions covers reading and sketching the graph of a more general rational function, including its asymptotes.
Multiplying and Dividing Rational Expressions and Adding and Subtracting Rational Expressions cover the four basic operations on rational expressions, treating them like fractions built from polynomials.
Solving Rational Equations closes the chapter with the techniques (and the extraneous-solution check they require) for solving equations that contain rational expressions.
The five lessons here, including Graphing Rational Functions, Adding and Subtracting Rational Expressions, and Solving Rational Equations, each open as an Algebra 2 worksheet in the page. Problems are scored as they are answered, so an extraneous solution left unchecked is flagged at that question. All five are free to work through.
Frequently asked questions
Inverse Variation opens with the simplest rational relationship, where one quantity rises as another falls. Graphing Rational Functions covers asymptotes, holes, and intercepts, then Multiplying and Dividing Rational Expressions and Adding and Subtracting Rational Expressions treat these expressions like fractions, with the same need for a common denominator. Solving Rational Equations closes the chapter, including the check for extraneous solutions that the method makes necessary. It sits in Algebra (A) and Functions (F) in the high school Common Core.
Inverse variation describes a relationship where one quantity increases as the other decreases, following the form y = k/x for some constant k.
Identify the vertical asymptotes (where the denominator equals zero) and the horizontal or slant asymptote (from comparing the numerator and denominator’s degrees), then plot a few key points.
Factor both expressions fully, cancel any common factors, then multiply numerators and denominators together (for multiplication) or multiply by the reciprocal (for division).
Find a common denominator, just like adding or subtracting numerical fractions, then combine the numerators over that shared denominator.
Multiply every term by the least common denominator to clear all fractions, solve the resulting polynomial equation, then check for extraneous solutions.