How to find point of discontinuity?
Understand the Problem
The question is asking for the method to identify points where a function is discontinuous. This involves understanding the definitions of continuity and applying them to find such points in a function's domain.
Answer
Factor and simplify the rational function; solve for x-values that make the denominator zero.
To find the point of discontinuity, you need to factor the numerator and denominator, cancel common factors, and solve for the x-values that make the remaining denominator zero.
Answer for screen readers
To find the point of discontinuity, you need to factor the numerator and denominator, cancel common factors, and solve for the x-values that make the remaining denominator zero.
More Information
A point of discontinuity occurs in a rational function when both the numerator and denominator are zero at the same x-value. By understanding and removing these common factors, you can identify these critical points.
Tips
Common mistakes include forgetting to simplify the function entirely before finding discontinuities or not correctly re-substituting x-values to check for y at discontinuities.
Sources
- The web page with info on - Example Source - expii.com
- How to find the point of discontinuity - StudyPug - studypug.com
- Precalculus : Find a Point of Discontinuity - Varsity Tutors - varsitytutors.com
