Asymptotes in Pre-Calculus

dbond10, Sep 17, 2024

An overview of recognizing and determining asymptotes in rational functions, exponential functions, and hyperbolic functions

Table of Contents

  1. Chapter 1 - Introduction to Asymptotes
    1. Asymptotes
    2. Vertical asymptotes
    3. Asymptotes
    4. Questions on asymptotes
  2. Chapter 2 - Asymptotes in Rational Functions
    1. Asymptotes for rational function
    2. Horizontal Asymptotes of Rational Functions
    3. Formal Limits for Vertical Asymptotes
  3. Chapter 3 - Asymptotes of Exponential Functions
    1. Exponential Asymptote
    2. Domain Range Asymptote Intercepts of Logarithmic Functions
  4. Chapter 4 - Asymptotes of Hyperbolic Functions
    1. Hyperbola
    2. Investigating Hyperbola
    3. Defining a Hyperbola

1.

Chapter 1 - Introduction to Asymptotes

  • 1. Asymptotes
  • 2. Vertical asymptotes
  • 3. Asymptotes
  • 4. Questions on asymptotes

1.1.

Asymptotes

Explore the nature of asymptotes by looking at 5 different functions. Just click the button next to the function to display or hide its graph.
Asymptotes
– Lindsay

1.2.

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1.3.

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1.4.

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2.

Chapter 2 - Asymptotes in Rational Functions

  • 1. Asymptotes for rational function
  • 2. Horizontal Asymptotes of Rational Functions
  • 3. Formal Limits for Vertical Asymptotes

2.1.

Asymptotes for rational function

What kind of asymptotes a rational function can have?
Asymptotes for rational function
– Mathguru, Mäkiö

2.2.

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2.3.

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3.

Chapter 3 - Asymptotes of Exponential Functions

  • 1. Exponential Asymptote
  • 2. Domain Range Asymptote Intercepts of Logarithmic Functions

3.1.

Exponential Asymptote

– Brian

3.2.

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4.

Chapter 4 - Asymptotes of Hyperbolic Functions

  • 1. Hyperbola
  • 2. Investigating Hyperbola
  • 3. Defining a Hyperbola

4.1.

Hyperbola

Hyperbola - a, b and c
This is a East-West Hyperbola. As you can see, the points A and A' are the vertices of the Hyperbola, C and C' are the foci of the Hyperbola, B and B' are the heights of the fundamental box from the centre of the Hyperbola.[br][br]Move ONLY the 2nd and the 4th slider to see how increasing the values affect the hyperbola :)
– Seow Ryan

4.2.

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4.3.

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