POI-Discontinuities Practice

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Practice for Points of Interest - Discontinuities.

1 : Consider the following graph.

Does the above graph have any hole discontinuities?

Yes No

1.1 : What is the approximate $x$ -value of the hole? $\answer {-2.5}$

A hole is the type of discontinuity that is a single missing point in an otherwise continuous graph. This may not look like it quite right (another example of graphing being misleading, but not on purpose this time) but the $x$ -value is actually $-2.5$ .

1.1.1 : Is there a jump discontinuity?

Yes No

1.1.1.1 : What is the approximate $x$ -value of the jump discontinuity? $\answer {1.5}$

A jump discontinuity is the type of discontinuity that has a finite vertical jump between the end points.

1.1.1.1.1 : Is there an infinite discontinuity?

Yes No

1.1.1.1.1.1 : What is the approximate $x$ -value of the infinite discontinuity? $\answer {5}$

An infinite discontinuity is the type of discontinuity that has a vertical asymptote.