A graph that is continuous means we can draw the entire thing without lifting our pencil from the paper. It has no holes, no breaks, no jumps in the graph. The continuous graph is predictable and makes a good bridge because a person "driving" over it would not fall through or fall off.
On the other hand....a discontinuous graph is the exact opposite. We have four types of discontinuities divided into two families.
- Removable Discontinuities
- Wherever there is a HOLE in the graph, it is called a point discontinuity.
- Non-Removable Discontinuities
- Jump discontinuities includes a break in the graph.
- Oscillating behavior occurs when the graph is "wiggly" and unpredictable.
- Infinite discontinuity occurs whenever there is a vertical asymptote and is also known as unbounded behavior.
(Images from education.com, wyzant.com, and en.wikipedia.org)
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