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Limits at infinity - Polynomial functions

PowerPoint lesson on limits at infinity and horizontal asymptotes for polynomial and rational functions, taught through fully worked examples.
Limits at infinity - Polynomial functions video preview
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Look Inside · 10 pages

Lesson cover introducing limits at infinity and the objective of understanding horizontal asymptotes
Opening slide and lesson objective
Introduction slide defining limits at infinity as function behavior as x approaches positive or negative infinity
Definition of limits at infinity
Limit properties slide covering sums, differences, products, quotients, constant multiples, and rational powers
Five algebraic properties of limits
Fact 1 slide explaining why c/x^r approaches zero for positive r as x approaches positive or negative infinity
Fact 1: limits of constants divided by powers
Fact 2 slide linking polynomial end behavior to the leading term and defining horizontal asymptotes
Fact 2 and the horizontal asymptote definition
Worked example finding the horizontal asymptote y = 1/2 for (x + 2)/(2x + 3) by dividing terms by x
First worked horizontal asymptote example
Method 1 example dividing (x + 3)/(x^2 + 1) by x^2 to find a limit of zero and horizontal asymptote y = 0
Second example, method 1: divide by x squared
Method 2 example factoring out x^2 in (x + 3)/(x^2 + 1) to find zero and the horizontal asymptote y = 0
Second example, method 2: factor out x squared
Worked example dividing (x - 3x^3)/(2x^3 - x + 5) by x^3 to find the horizontal asymptote y = -3/2
Third example, first method: divide by x cubed
Method 2 example factoring out x^3 in (x - 3x^3)/(2x^3 - x + 5) to find horizontal asymptote y = -3/2
Third example, second method: factor out x cubed
Grades
Grades 10–12, High School
File type
Microsoft PowerPoint
Use
Digital activity

Updated Oct 26, 2026

Subject
Math, Calculus
Topic
Limits, Precalculus
Resource types
Teacher Tools, Lesson Plans
Use
Digital activity

About this resource

What's inside this resource

PowerPoint presentation, 13 slides explaining how to calculate the limit of polynomial functions, as the function approaches either to positive or negative infinity.

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Limits at infinity - Polynomial functions. Worksheet Limits at infinity - Polynomial functions. WorksheetLimits at infinity - transcendental functions - Worksheet Limits at infinity - transcendental functions - WorksheetLimits at Infinity – Exponential Functions Worksheet Limits at Infinity – Exponential Functions WorksheetLimits at infinity - transcendental functions Limits at infinity - transcendental functions

In the classroom

Teaching tips & learning objectives

Learning objectives

  • Evaluate limits of polynomial and rational functions as x approaches positive or negative infinity
  • Determine horizontal asymptotes from limits at infinity
  • Apply sum, product, quotient and constant multiple limit properties

Skills covered

  • Algebraic simplification — dividing numerator and denominator by the highest power of x before taking the limit

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Resource details

Concepts & topics

Core concepts

  • Limits at infinity
  • Horizontal asymptotes
  • Limit properties
  • Rational functions
  • Polynomial functions

Topics

Limits Precalculus positive infinity negative infinitive polynomial functions

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Categories this resource belongs to

Math Lesson Plans Addition and Subtraction Lesson Plans Algebra Lesson Plans Decimals Lesson Plans Early Math Lesson Plans

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