2. Disappearing Asymptotes
The Visual Answers

3. Disappearing Asymptotes:
Consider the graph of the function defined by:

5. And then, the graph of the function defined by:

6. hole in the graph!

7. Again:
hole in the graph!

8. Consider the graph of a series of rational functions with denominator of the form x – a, where 1 < a < 2.
Keep your eye on:
1) the position of the vertical asymptote
2) the diagonal distance between the two “halves” of the graph.

21. hole in the graph!

22. Extension:
What would happen if we explored the same relationship from the left side of the asymptote? i.e.
How would the graph change, etc.?