Disappearing Asymptotes The Visual Answers Disappearing Asymptotes: Consider the graph of the function defined by:

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Presentation transcript:

Disappearing Asymptotes The Visual Answers

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

And then, the graph of the function defined by:

hole in the graph!

Again: hole in the graph!

Now consider: GRAPHICALLY !

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.

hole in the graph!

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.?