How to Determine if a Limit Exists by the Graph of a Function

We are going to use some examples of functions and their graphs to show how we can determine whether the limit exists as x approaches a particular number.

    There are four different ways to determine if a limit exists by looking at the graph for the function. The first, which shows that the limit DOES exist, is if the graph has a hole in the line, with a point for that value of x on a different value of y. If this happens, then the limit exists, though it has a different value for the function than the value for the limit. Please click on the image for a better understanding.

    If there is a hole in the graph at the value that x is approaching, with no other point for a different value of the function, then the limit does still exist. Please see the graph for a better understanding.

    If the graph has a vertical asymptote, that is two lines approaching the value of the limit that continue up or down without bounds, then the limit does not exist. Please click on the image for a better understanding.

    If the graph is approaching two different numbers from two different directions, as x approaches a particular number then the limit does not exist. It cannot be two different numbers. Please click on the image for a better understanding.

    Things You'll Need

    • Paper
    • and Pencil

Related Articles

The Best STEM Kits to Get Your Kids Started With Coding
How to Find Vertical & Horizontal Asymptotes
How to Write the equation of a Linear Function whose...
How to Find the Inverse of a Function
How to Sketch the Graph of Square Root Functions, (...
How to Know the Difference between a Vertical Asymptote,...
How to Find the Minimum or Maximum in a Quadratic Equation
How to Find a Tangent Line to a Curve
How to Find the X Intercept of a Function
How to Solve Inequalities
Ways to Tell if Something Is a Function
How to Find the Point of Discontinuity in Algebra II
How to Analyze Graphs
To Calculate Arcsine, What Buttons Do You Press on...
What is Function Notation?
How to Find the Domain Range of a Parabola Parameter...
How to Calculate SSE
How to Find Horizontal Asymptotes of a Function on...
How to Find the Vertical Tangent
How to Calculate the Wronskian
How to Explain Input & Output Tables in Algebra