Rational Functions: Tutorials, Graphers & Solved Practice
Welcome to the Rational Functions hub. Explore tutorials, interactive graphers, worked examples, and practice problems covering the full range of rational-function topics: domain and intercepts, vertical/horizontal/slant asymptotes, transformations, graph identification, simplification, and rational inequalities.
Core Tutorials & Interactive Graphers
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Rational Functions: Domain, Intercepts, Asymptotes & Holes
A complete guide to the key features of rational functions, including how to find holes and intercepts.
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Horizontal Asymptotes of Rational Functions – Interactive
Explore how the degrees of numerator and denominator determine horizontal asymptotes.
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Vertical Asymptotes of Rational Functions – Interactive
Practice finding vertical asymptotes by identifying uncanceled zeros of the denominator.
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Slant Asymptotes of Rational Functions – Interactive
Identify and graph oblique asymptotes when the numerator degree exceeds the denominator by one.
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Finding Rational Functions (Tutorial 1)
Construct a rational function from its graph or given properties.
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Interactive Rational Functions & Transformations
Visualize how changes to numerator and denominator affect the graph.
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Solving Rational Inequalities: 6 Step-by-Step Examples
Sign-table method, critical points, combined fractions, and absolute values.
Rational Expressions: Domain, Simplification & Practice
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Rational Expressions & Their Domain: Examples & Practice
Definition of rational expressions and how to find the domain by excluding zeros of the denominator.
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Simplify Rational Expressions Calculator
Online tool to add, subtract, multiply, divide, and simplify rational expressions, with a manual walkthrough.
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Simplify Rational Expressions (Tutorial)
Grade 11 examples with detailed step-by-step solutions for simplifying complex algebraic fractions.
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Reducing Rational Expressions: Practice & Solutions
Practice factoring numerators and denominators and canceling common factors, with worked answers.
Graph Identification
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Identify Graphs of Rational Functions: Worked Examples
Match a rational function to its graph using vertical/horizontal asymptotes, x-intercepts, and multiplicity.