# Functions, Graphs, and Limits

# Functions, Graphs, and Limits Table of Contents

Functions, Graphs, and Limits

Topics

Functions, Graphs, and Limits Examples

Functions, Graphs, and Limits Exercises

Limits

Limits Help

Functions Are Your Friend

Functions Are Your Friend Help

Functions Are Your Friend Exercises

Graphing and Visualizing Limits

Graphing and Visualizing Limits Help

Graphing and Visualizing Limits Exercises

Piecewise Functions and Limits

Piecewise Functions and Limits Help

Piecewise Functions and Limits Exercises

One-Sided Limits

One-Sided Limits Help

One-Sided Limits Examples

One-Sided Limits Exercises

Limits via Tables

Limits via Tables Help

Limits via Tables Exercises

Limits via Algebra

Limits via Algebra Help

Limits via Algebra Exercises

All About Asymptotes

All About Asymptotes Help

Vertical Asymptotes

Vertical Asymptotes Help

Vertical Asymptotes Exercises

Finding Vertical Asymptotes

Finding Vertical Asymptotes Help

Finding Vertical Asymptotes Examples

Finding Vertical Asymptotes Exercises

Vertical Asymptotes vs. Holes

Vertical Asymptotes vs. Holes Help

Vertical Asymptotes vs. Holes Examples

Vertical Asymptotes vs. Holes Exercises

Limits at Infinity

Limits at Infinity Help

Natural Numbers

Natural Numbers Help

Limits Approaching Zero

Limits Approaching Zero Help

Estimating a Circle

Estimating a Circle Help

The Cantor Set and Fractals

The Cantor Set and Fractals Help

Limits of Functions at Infinity

Limits of Functions at Infinity Help

Limits of Functions at Infinity Examples

Limits of Functions at Infinity Exercises

Horizontal, Slant, and Curvilinear Asymptotes

Horizontal, Slant, and Curvilinear Asymptotes Help

Horizontal Asymptoes

Horizontal Asymptoes Help

Slant Asymptotes

Slant Asymptotes Help

Curvilinear Asymptotes

Curvilinear Asymptotes Help

Topics

Functions, Graphs, and Limits Examples

Functions, Graphs, and Limits Exercises

Limits

Limits Help

Functions Are Your Friend

Functions Are Your Friend Help

Functions Are Your Friend Exercises

Graphing and Visualizing Limits

Graphing and Visualizing Limits Help

Graphing and Visualizing Limits Exercises

Piecewise Functions and Limits

Piecewise Functions and Limits Help

Piecewise Functions and Limits Exercises

One-Sided Limits

One-Sided Limits Help

One-Sided Limits Examples

One-Sided Limits Exercises

Limits via Tables

Limits via Tables Help

Limits via Tables Exercises

Limits via Algebra

Limits via Algebra Help

Limits via Algebra Exercises

All About Asymptotes

All About Asymptotes Help

Vertical Asymptotes

Vertical Asymptotes Help

Vertical Asymptotes Exercises

Finding Vertical Asymptotes

Finding Vertical Asymptotes Help

Finding Vertical Asymptotes Examples

Finding Vertical Asymptotes Exercises

Vertical Asymptotes vs. Holes

Vertical Asymptotes vs. Holes Help

Vertical Asymptotes vs. Holes Examples

Vertical Asymptotes vs. Holes Exercises

Limits at Infinity

Limits at Infinity Help

Natural Numbers

Natural Numbers Help

Limits Approaching Zero

Limits Approaching Zero Help

Estimating a Circle

Estimating a Circle Help

The Cantor Set and Fractals

The Cantor Set and Fractals Help

Limits of Functions at Infinity

Limits of Functions at Infinity Help

Limits of Functions at Infinity Examples

Limits of Functions at Infinity Exercises

Horizontal, Slant, and Curvilinear Asymptotes

Horizontal, Slant, and Curvilinear Asymptotes Help

Horizontal Asymptoes

Horizontal Asymptoes Help

Slant Asymptotes

Slant Asymptotes Help

Curvilinear Asymptotes

Curvilinear Asymptotes Help

Finding Horizontal/Slant/Curvilinear Asymptotes

Finding Horizontal/Slant/Curvilinear Asymptotes Help

Finding Horizontal/Slant/Curvilinear Asymptotes Examples

Finding Horizontal/Slant/Curvilinear Asymptotes Exercises

How to Draw Rational Functions from Scratch

How to Draw Rational Functions from Scratch Help

How to Draw Rational Functions from Scratch Examples

How to Draw Rational Functions from Scratch Exercises

Comparing Functions

Comparing Functions Help

Power Functions vs. Polynomials

Power Functions vs. Polynomials Help

Power Functions vs. Polynomials Examples

Power Functions vs. Polynomials Exercises

Polynomials vs. Logarithmic Functions

Polynomials vs. Logarithmic Functions Help

Polynomials vs. Logarithmic Functions Examples

Polynomials vs. Logarithmic Functions Exercises

Manipulating Limits

Manipulating Limits Help

The Basic Properties

The Basic Properties Help

The Basic Properties Examples

The Basic Properties Exercises

Multiplication by a Constant

Multiplication by a Constant Help

Multiplication by a Constant Examples

Adding and Subtracting Limits

Adding and Subtracting Limits Help

Adding and Subtracting Limits Examples

Adding and Subtracting Limits Exercises

Multiplying and Dividing Limits

Multiplying and Dividing Limits Help

Multiplying and Dividing Limits Examples

Multiplying and Dividing Limits Exercises

Powers and Roots of Limits

Powers and Roots of Limits Help

Powers and Roots of Limits Examples

Powers and Roots of Limits Exercises

In the Real World

In the Real World Help

I Like Abstract Stuff; Why Should I Care?

I Like Abstract Stuff; Why Should I Care? Help

How to Solve a Math Problem

How to Solve a Math Problem Help

Terms

Best of the Web

Module Quizzes

Module Flashcards

Fun Fun Functions

Fun Fun Functions Flashcards

Fun Fun Functions True or False

Approachable

Approachable Flashcards

Approachable True or False

What's Your Function?

What's Your Function? Flashcards

What's Your Function? True or False

Handouts

Finding Horizontal/Slant/Curvilinear Asymptotes Help

Finding Horizontal/Slant/Curvilinear Asymptotes Examples

Finding Horizontal/Slant/Curvilinear Asymptotes Exercises

How to Draw Rational Functions from Scratch

How to Draw Rational Functions from Scratch Help

How to Draw Rational Functions from Scratch Examples

How to Draw Rational Functions from Scratch Exercises

Comparing Functions

Comparing Functions Help

Power Functions vs. Polynomials

Power Functions vs. Polynomials Help

Power Functions vs. Polynomials Examples

Power Functions vs. Polynomials Exercises

Polynomials vs. Logarithmic Functions

Polynomials vs. Logarithmic Functions Help

Polynomials vs. Logarithmic Functions Examples

Polynomials vs. Logarithmic Functions Exercises

Manipulating Limits

Manipulating Limits Help

The Basic Properties

The Basic Properties Help

The Basic Properties Examples

The Basic Properties Exercises

Multiplication by a Constant

Multiplication by a Constant Help

Multiplication by a Constant Examples

Adding and Subtracting Limits

Adding and Subtracting Limits Help

Adding and Subtracting Limits Examples

Adding and Subtracting Limits Exercises

Multiplying and Dividing Limits

Multiplying and Dividing Limits Help

Multiplying and Dividing Limits Examples

Multiplying and Dividing Limits Exercises

Powers and Roots of Limits

Powers and Roots of Limits Help

Powers and Roots of Limits Examples

Powers and Roots of Limits Exercises

In the Real World

In the Real World Help

I Like Abstract Stuff; Why Should I Care?

I Like Abstract Stuff; Why Should I Care? Help

How to Solve a Math Problem

How to Solve a Math Problem Help

Terms

Best of the Web

Module Quizzes

Module Flashcards

Fun Fun Functions

Fun Fun Functions Flashcards

Fun Fun Functions True or False

Approachable

Approachable Flashcards

Approachable True or False

What's Your Function?

What's Your Function? Flashcards

What's Your Function? True or False

Handouts