How to tell if a function is continuous without graphing?
Understand the Problem
The question is asking for methods to determine the continuity of a function without needing to graph it, which likely involves using mathematical definitions and properties of continuity.
Answer
Check left and right limits and ensure they equal the function value at the point.
To determine if a function is continuous without graphing, you need to check the left and right limits at a specific point and ensure they are equal to each other and to the value of the function at that point.
Answer for screen readers
To determine if a function is continuous without graphing, you need to check the left and right limits at a specific point and ensure they are equal to each other and to the value of the function at that point.
More Information
A function is said to be continuous at a point if the function is defined at that point, the left and right limits exist, and all three are equal.
Tips
A common mistake is forgetting to check that the function is defined at the point where you're assessing continuity.
Sources
- Determine if a Function is Continuous Using Limits - VarsityTutors - varsitytutors.com
- How to Determine Whether a Function Is Continuous or Discontinuous - Dummies - dummies.com
- 2.6: Continuity - Mathematics LibreTexts - math.libretexts.org
