POI-Discontinuities Practice

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Practice for Points of Interest - Discontinuities.

Consider the following graph.

Does the above graph have any hole discontinuities?

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 $-2.5$ .

Is there a jump discontinuity?

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.

Is there an infinite discontinuity?

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.

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defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
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prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
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infinity	$\infty$
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arctan	$\arctan\left(\blue{[?]}\right)$
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Omega	$\Omega$

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