Disappearing Asymptotes

The Visual Answers

Disappearing Asymptotes:

Consider the graph of the function defined by:

212

xx

y

And then, the graph of the function defined by:

112

xx

y

hole in the graph!

Again:

212

xx

y112

xx

y

hole in the graph!

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.?

212

xx

y