Math Plane
---->>>FLIGHT DELAYS!!
Recently, Mathplane has been experiencing slow page loads.
Sorry for the delays. We are working on the traffic and server issues.
Thank you for your patience and persistence!
- Home
- Airport Terminal
- Gate 1/Pre-algebra
- 3rd Grade Worksheets
- Greatest Common Factor & Least Common Multiple
- Decimals
- Decimals Puzzle
- Fractions Exercises
- Mixed Numbers
- Percentages
- Converting Fractions Decimals Percentages
- Word Problems
- Angles & Triangles Exercise
- Middle School Geometry
- Conversions
- Negative Numbers
- Mean Median Mode
- Scientific Notation
- Pre-Algebra Review 1
- Pre-Algebra Review 2
- Pre-Algebra Review 3
- Gate 2/Algebra
- Numbers
- Algebra Preview
- Algebra Preview 2
- Exponents & Roots and Order of Operations
- Negative Exponents and Variables
- Exponents and Exponential Equations
- Inequalities and Number Line
- Absolute Value and Inequalities
- Absolute Value and Inequalities Videos
- Linear Equations
- Linear Equations 2
- Linear Systems
- Linear Systems 2
- Slope & Linear Equations Videos
- Linear Programming (Optimization)
- Story Graphs
- Inverse Functions
- Average Midpoint Distance Test
- Radicals
- Intro to Polynomials
- Factoring Quadratics
- Simplifying Rational Polynomials
- Simplifying Rational Expressions
- f(x) and Piecewise functions
- Probability
- Word Problems
- Word Problems 2
- Algebra Word Problem Videos
- Algebra Word Problem Videos 2
- Domain, Range, Functions, & Relations
- Algebra Review 1
- Algebra Review 2
- Algebra Review 3
- Algebra Review 4
- Algebra Review 5
- Gate 3/Geometry
- Geometry Introduction
- Angle Properties
- Triangle Characteristics
- Triangle Restrictions
- Polygons
- Special Quadrilaterals 1
- Special Quadrilaterals 2
- Logic and Reasoning
- Always Sometimes Never
- Congruent Triangles Topics
- Proofs & Postulates 0
- Proofs & Postulates 1
- Proofs & Postulates 2
- Diagramless and Detour Proofs
- Indirect Proofs
- Equidistance Theorem
- Parallel Lines Cut by Transversals
- Planes Properties and Proofs
- Triangle Median Altitude Bisectors
- Midpoint and Distance
- Similarity and Proportions 1
- Similarity and Proportions 2
- Similarity and Proportions 3
- Similarity and Proportions 4
- Means Extremes and Right Triangles
- Pythagorean Theorem & Distance
- Pythagorean Theorem 2 (more questions)
- Area and Perimeter of Polygons 1
- Area and Perimeter of Polygons 2
- Area and Perimeter of Complex Shapes
- Area of Shapes (Honors)
- Surface Area
- Volume
- Surface Area and Volume (Advanced)
- Circles Introduction
- Circles and Geometry
- Circles and Inscribed Figures
- Circles Review (Honors)
- Circles Review (Advanced)
- Circles Practice Test
- Word Problems
- Coordinate Geometry 1
- Coordinate Geometry 2
- Coordinate Geometry 3 Drawing Exercise
- Coordinate Geometry 4 - Advanced
- Locus of Points
- Geometry Construction Videos 1 - Intro
- Geometry Construction Videos 2- Intermediate
- Geometry Construction Videos 3- Advanced
- Geometry Review 1
- Geometry Review 2
- Geometry Review 3
- Geometry Review 4
- Geometry Review 5 Midterm
- Gate 4/Trigonometry
- Angle Measurement
- Arc Length & Sector Area
- Right Triangle Review
- Trigonometry Introduction
- Word Problems
- Unit Circle and Trigonometry Functions
- Inverse Trig Values
- Law of Sines and Cosines I
- Law of Sines and Cosines II
- Law of Sines and Cosines III
- Navigation
- Periodic Functions I - Sine (Graphs)
- Periodic Functions II - Cosine
- Periodic Functions III - Tangent
- Periodic Functions IV - Reciprocals
- Periodic Inverse Functions
- Periodic Trig Function Models
- Trig Identities I - Introduction
- Trig Identities II - Double Angles
- Trig Identities III - Solving and Graphing
- Trig Identities IV - Review Test
- Trig Identities V - Honors
- Polar Coordinates and Complex System
- Polar Equations and Graphs
- Trigonometry Extras
- Trigonometry Review 1
- Trigonometry Review 2
- Trigonometry Review 3
- Trigonometry Review 4
- Gate 5/Algebra II
- Algebra I/Geometry Review
- Algebra II Preview
- Inverses
- Graphing I - Parent Functions & Transformations
- Graphing II - Translation, Reflection, & Rotation
- Graphing III Identifying Functions
- Graphing Functions Videos
- Absolute Value Graphing Topics
- Double Absolute Values
- Composite Functions Topics
- Quadratics Overview
- Completing the Square & Quadratic Formula
- Identifying Quadratic Equations from Points
- Quadratics Practice Test
- Comparing Equations
- Modeling Word Problems
- Polynomials: Factors, Roots & Theorems I
- Polynomials: Factors, Roots, & Theorems II
- Polynomials: Factors, Roots, & Theorems III (Honors)
- Solving Rational Equations
- Sketching Rational Expressions I
- Sketching Rational Expressions II
- Reciprocal Functions
- Direct and Inverse Variation
- Word Problems
- Conics I - Circles & Ellipses
- Conics II - Hyperbolas and Parabolas
- Conics III - Review Properties
- Conics IV - Systems
- Conics V - More Advanced
- Conics VI - Honors Topics
- Rotation of Axes
- Analytic Geometry
- Semicircles
- Transformations of Functions (Advanced)
- Matrix I Examples
- Matrix II and Determinants
- Matrix III Coordinate Geometry
- Imaginary and Complex Numbers
- Rational Exponents & Radical Equations
- Variable Exponents and Higher Roots
- Exponents and Exponential Equations (Honors)
- Logarithms and Exponents I
- Logarithms and Exponents II
- Logarithms and Exponents III (Advanced)
- Growth Decay Interest & Half-Life
- Logarithms Practice Test
- Combinations, Permutations, & Counting
- Sequences & Series I
- Sequences & Series II
- Sequences & Series III
- Binomial Expansion Theorem
- Math Induction
- Parametric Equations
- Vectors I
- Vectors II
- 3 Dimensional Space and Vectors
- 3-Dimensional Space and Sketches
- Partial Fractions
- Algebra II Notation & Operations Puzzle
- Algebra II review 1
- Algebra II review 2
- Algebra II review 3
- Algebra II review 4
- Algebra II review 5
- Algebra II review 6
- Algebra II review Equations and Inequalities
- Pre-Calculus Advanced Questions
- Gate 6/Calculus
- Algebra II/Trig Practice Exam
- Limits and Asymptotes
- Definition of Instantaneous Rate of Change
- Continuity & Differentiability
- Intro to Derivatives
- Derivative Rules: Product/Quotient, Chain & Power
- Derivative Rules: Trigonometry Functions
- Chain Rule
- Derivative Rules: Log, Exponents, & Trig functions
- Applications of derivatives
- Mean Value Theorem
- Derivative max/min word problems
- Critical Values from Derivatives
- Sketching Graphs 1: 1st and 2nd derivatives
- Sketching Graphs 2: anti-derivatives
- Position Velocity Speed Acceleration
- Implicit Differentiation
- Related Rates of Change
- Using Derivatives in Economics
- Intro to Integrals
- Antiderivatives and Integrals
- Fundamental Theorem of Calculus (Part 1)
- Trapezoid Rule
- Definite Integrals & Fundamental Theorem of Calculus (Part 2)
- Definite Integrals Concepts and Applications
- Definite Integrals and Area Between Curves
- Natural log and e
- Improper Integrals
- Volumes of Solids 1
- Volumes of Solids 2
- Arc Length
- Trig Substitutions
- Separable Differential Equations
- Using Integrals in Economics
- Series Convergence and Divergence
- Calculus Extras
- Calculus Review 1
- Calculus Review 2
- Calculus Review 3 AP Multiple Choice
- Calculus Review 4 AP Free Response
- Calculus Review 5 AP Multiple Choice 2
- Gate 7/Statistics
- Airport Terminal 2
- Gate A/Instant Answers
- Math Resources: Definitions
- Math Resources: Community Help
- Math Resources: Calculators
- TI nspire cx cas calculator tutorial 0
- TI nspire cx cas calculator tutorial 1
- TI nspire cx cas calculator tutorial 2
- TI nspire cx cas calculator tutorial 3
- TI nspire cx cas calculator tutorial 4
- TI nspire cx cas calculator tutorial 5
- TI nspire cx cas calculator questions
- TI nspire cx cas calculator project 1
- TI nspire cx cas calculator project 2
- TI nspire cx cas calculator project 3
- TI nspire cx cas calculator project 4
- TI nspire cx cas calculator project 5
- TI nspire cx cas calculator project 6
- Gate B/ACT/SAT Topics
- ACT subjects to know
- SAT subjects to know
- ACT/SAT Quick Quiz 1
- ACT/SAT Quick Quiz 2
- ACT/SAT Quick Quiz 3
- ACT/SAT Quick Quiz 4*
- Mental Math Speed Drills
- ACT Practice Test 1
- ACT Practice Test 2
- ACT Practice Test 3
- ACT Practice Test 4
- ACT Practice Test 5
- ACT Geometry Practice Test 1
- ACT Trigonometry Practice Test 1
- SAT Practice Test 1
- SAT Practice Test 2
- SAT Practice Test 3
- SAT Practice Test 4*
- SAT Practice Test 5
- Challenging ACT/SAT practice test 1
- Challenging ACT/SAT practice test 2
- ACT Hidden Message Puzzle 1
- ACT Hidden Message Puzzle 2
- Overview & Random Suggestions
- SAT Subject Test Level 2 Topics to know
- SAT Math Level 2 Practice Test A
- SAT Math Level 2 Practice Test B
- SAT Math Level 2 Practice Test C
- SAT Math Level 2 Practice Test D
- SAT Math Level 2 Practice Test E
- SAT Math Level 2 Practice Test F
- SAT 2 Hidden Message Puzzle
- Gate C/Math Places around the Virtual World
- Gate D/Webcomics
- Math Comics Archive (Fall 2011)
- Math Comics Archive (Winter 2012)
- Math Comics Archive (Spring 2012)
- Math Comics Archive (Summer 2012)
- Math Comics Archive (Fall 2012)
- Math Comics Archive (Winter 2013)
- Math Comics Archive (Spring 2013)
- Math Comics Archive (Summer 2013)
- Math Comics Archive (Fall 2013)
- Math Comics Archive (Winter 2014)
- Math Comics Archive (Spring 2014)
- Math Comics Archive (Summer 2014)
- Math Comics Archive (Fall 2014)
- Math Comics Archive (Winter 2015)
- Math Comics Archive (Spring 2015)
- Math Comics Archive (Summer 2015)
- Math Comics Archive (Fall 2015)
- Math Comics Archive (Winter 2016)
- Math Comics Archive (Spring 2016)
- Math Comics Archive (Summer 2016)
- Math Comics Archive (Fall 2016)
- Math Comics Archive (Winter 2017)
- Math Comics Archive (Spring 2017)
- Math Comics Archive (Summer 2017)
- Math Comics Archive (Fall 2017)
- Math Comics Archive (Winter 2018)
- Math Comics Archive (Spring 2018)
- Math Comics Archive (Summer 2018)
- Math Comics Archive (Fall 2018)
- Math Comics Archive (Winter 2019)
- Math Comics Archive (Spring 2019)
- Math Comics Archive (Summer/Fall 2019)
- Math Comics Archive (Winter/Spring 2020)
- Gate E/Destinations
- Travel Checklist
- Featured Destination math enrichment
- Random Places to Visit
- 2012 Puzzle
- Super Bowl XLVI
- I (Heart) Symmetry
- Prime Time
- Play Ball
- When in Rome
- Live at the Mobius Strip
- Trick Shots in the Pool Hall
- 2013 Puzzle
- 8 - wonder of the world
- In the Dog house
- parallelogram parking
- slice of pi
- April 15th Tax Relief
- Math Photos
- 2014 Puzzle
- 2015 Puzzle
- What are the odds?
- In-Flight Entertainment (Videos)
- Spare Parts
- spare parts 24
- spare parts 23
- spare parts 22
- spare parts 21
- spare parts 20
- spare parts 19
- spare parts 18
- spare parts 17
- spare parts 16
- spare parts 15
- spare parts 14
- spare parts 13
- spare parts 12
- spare parts 11
- spare parts 10
- spare parts 9
- spare parts 8
- spare parts 7
- spare parts 6
- spare parts 5
- spare parts 4
- spare parts 3
- spare parts 2
- spare parts 1
- Travel Log Collection
- About Us
- 2013 US Road Trip with Oscar the Dog
- 2013 US Road Trip with Oscar (Part II)
- 2014 US South Road Trip with Oscar
- 2014 US Summer Road Trip with Oscar (East)
- 2014 US Summer Road Trip with Oscar (South)
- 2015 Summer Road Trip with Oscar (Canada West)
- 2015 Summer Road Trip with Oscar (Canada East)
- 2017 Summer Road Trip with Norway the Husky (US - Canada East)
- 2017 Summer Road Trip with Norway the Husky (Canada - US West)
- 2018 Summer Road Trip with Norway the Husky (US - Canada East)
- 2018 Summer Road Trip with Norway the Husky (Canada - US West)
- 2019 US South Road Trip with Norway the Husky
- 2019 Summer Road Trip with Norway the Husky (around Lake Michigan)
- 2021 Summer Road Trip with Norway the Husky (The Heartland)
- 2022 Winter Road Trip with Norway the Husky (Route 66)
- 2023 Winter Road Trip with Norway the Husky (Route 66)
- Privacy
- Terms of Use
- Support
- Advertising
- Contact Us
- Bring Oscar
Sketching Rational Expressions II - End Behavior Asymptotes
This second part explores more complex graphs of rational expressions. Includes examples and practice exercises (with detailed solutions).
Click lower right to select panel.
Right click to view or save to desktop.
Math Comic #312 - "Hangman" (3-4-18)
___________________________
Download Free Complete Rational Expressions II .pdf file
___________________________________________
Connections
Free user friendly online graphing tool from desmos.com
*****
Are you preparing for the SAT or ACT?
Looking to improve standardized test scores?
Check out free practice questions in Gate B, or download test prep materials and support the mathplane site!
___________________________________________
Webcomic 13 - "Math Graphs and Skiing" (1-8-12)
___________________________________________
Information
- Parabolic Asymptote
- Cubic Asymptote
- Limits
- Factoring
- Synthetic division
<--- Quiz
<--- Solutions
