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Mathematics

442What is a Rational Expression?
443Evaluating Rational Expressions
444Finding Restricted Values
445Simplifying by Canceling Common Factors
446Simplifying with Monomial Factors
447Simplifying with Binomial Factors
448Simplifying with Trinomial Factors
449Simplifying Expressions with Opposite Factors
450Writing Simplified Expressions with Domain Restrictions
451Multiplying Rational Expressions: Basic Method
452Simplifying Before Multiplying
453Multiplying Complex Rational Expressions
454Dividing Rational Expressions: Multiply by Reciprocal
455Dividing and Simplifying in One Step
456Mixed Operations: Multiplication and Division Together
457Multiplying and Dividing with Negative Signs
458Applications of Multiplying and Dividing Rationals
459Adding Rationals with Like Denominators
460Subtracting Rationals with Like Denominators
461Finding the Least Common Denominator (LCD)
462Building Equivalent Rationals
463Adding Rationals with Unlike Denominators
464Subtracting Rationals with Unlike Denominators
465Simplifying Sums and Differences
466Working with Opposite Denominators
467Adding and Subtracting Three or More Rationals
468Applications of Adding and Subtracting Rationals
469What is a Complex Fraction?
470Simplifying Complex Fractions by Multiplying by the LCD
471Simplifying Complex Fractions by Simplifying Numerator and Denominator
472Complex Fractions with Single-Variable Expressions
473Complex Fractions with Multiple Terms
474Nested Complex Fractions
475Applications and Word Problems with Complex Fractions
476Introduction to Rational Equations
477Finding Restricted Values and Domain
478Solving by Cross-Multiplication
479Multiplying by the LCD Method
480Solving Equations with Multiple Terms
481Checking for Extraneous Solutions
482Rational Equations Leading to Quadratics
483Work and Rate Problems
484Distance-Rate-Time and Mixture Problems
485Introduction to Rational Functions
486Vertical Asymptotes
487Holes in Rational Functions
488Horizontal Asymptotes: Degree Rules
489Finding Horizontal Asymptotes by Leading Coefficients
490Slant (Oblique) Asymptotes
491Graphing Rational Functions with Asymptotes
492End Behavior of Rational Functions
493Domain and Range from Graphs
494Applications of Rational Functions

Mathematics

442What is a Rational Expression?
443Evaluating Rational Expressions
444Finding Restricted Values
445Simplifying by Canceling Common Factors
446Simplifying with Monomial Factors
447Simplifying with Binomial Factors
448Simplifying with Trinomial Factors
449Simplifying Expressions with Opposite Factors
450Writing Simplified Expressions with Domain Restrictions
451Multiplying Rational Expressions: Basic Method
452Simplifying Before Multiplying
453Multiplying Complex Rational Expressions
454Dividing Rational Expressions: Multiply by Reciprocal
455Dividing and Simplifying in One Step
456Mixed Operations: Multiplication and Division Together
457Multiplying and Dividing with Negative Signs
458Applications of Multiplying and Dividing Rationals
459Adding Rationals with Like Denominators
460Subtracting Rationals with Like Denominators
461Finding the Least Common Denominator (LCD)
462Building Equivalent Rationals
463Adding Rationals with Unlike Denominators
464Subtracting Rationals with Unlike Denominators
465Simplifying Sums and Differences
466Working with Opposite Denominators
467Adding and Subtracting Three or More Rationals
468Applications of Adding and Subtracting Rationals
469What is a Complex Fraction?
470Simplifying Complex Fractions by Multiplying by the LCD
471Simplifying Complex Fractions by Simplifying Numerator and Denominator
472Complex Fractions with Single-Variable Expressions
473Complex Fractions with Multiple Terms
474Nested Complex Fractions
475Applications and Word Problems with Complex Fractions
476Introduction to Rational Equations
477Finding Restricted Values and Domain
478Solving by Cross-Multiplication
479Multiplying by the LCD Method
480Solving Equations with Multiple Terms
481Checking for Extraneous Solutions
482Rational Equations Leading to Quadratics
483Work and Rate Problems
484Distance-Rate-Time and Mixture Problems
485Introduction to Rational Functions
486Vertical Asymptotes
487Holes in Rational Functions
488Horizontal Asymptotes: Degree Rules
489Finding Horizontal Asymptotes by Leading Coefficients
490Slant (Oblique) Asymptotes
491Graphing Rational Functions with Asymptotes
492End Behavior of Rational Functions
493Domain and Range from Graphs
494Applications of Rational Functions

← Mathematics

Lesson 491 of 3,121·12. Rational Expressions and EquationsPro lesson

Graphing Rational Functions with Asymptotes

Sketch rational function graphs by plotting asymptotes, holes, intercepts, and analyzing behavior near asymptotes.

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