Module 7: Rational Functions and Function Operations

 

This diagram shows a point of discontinuity and states “Points of discontinuity or ‘holes’ occur when a factor in both the numerator and denominator equals 0.” The image also shows an asymptote and states “Vertical asymptotes occur when a factor only in the denominator equals 0.” The image also shows an x-intercept and states “x-intercepts occur when a factor only in the numerator is equal to 0.”
Lesson 2 Summary

 

In this lesson you explored what happens on the graph of a rational function when it has a factor equal to 0 that occurs only in the numerator, only in the denominator, and in both the numerator and the denominator. If the 0 is only in the numerator, an x-intercept occurs. If the 0 is only in the denominator, an asymptote occurs. If the 0 shows up in both the numerator and denominator, a point of discontinuity occurs.

 

In the next lesson you will explore how the characteristics of a rational function can be used to sketch the function’s graph.