Module 7 - Limits and Infinity | ||||||||||
Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Lesson 4 | Self Test | ||||||||||
Lesson 7.2: Holes | ||||||||||
In this lesson you will investigate when a rational function has a hole in its graph and find a list of possible vertical asymptotes for a rational function.
In Lesson 7.1 you found the vertical asymptote of the rational function
![]() Holes vs. Asymptotes
When x = -2, the function is undefined because the denominator is 0 but the limit of the function as x approaches -2 from the left and from the right is a single specific value. Since
7.2.1 Evaluate
Displaying the Hole
In Lesson 7.1 you graphed the function
![]() There is no apparent hole shown in this window, but if you change the viewing window, the hole may be seen.
![]() The hole at (-2, 0.80) should now be visible. If you trace to x = -2, you can see that the function is undefined there. ![]()
The choice of Window values will determine whether or not a hole in the graph of a function will actually be visible on the graphing screen.
7.2.2 Find the vertical asymptote and the hole in the graph of
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