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Quiz 5

Question

The following graph has x- and y-axes and the scale for both axes is in units of one, labeled from minus five to plus five. Identify and classify each point of discontinuity.

Answer

The graph has an inifinite discontinuity at x equals minus one, a jump discontinuity at x equals one, and a removable discontinuity at x equals four.

Explanation

The graph consists of three segments.

The first segment begins at x equals minus five and y is close to but smaller than one. As it moves to the right, the graph decreases very slowly at first, then it decreases steeply around x passes minus two and the y-value becomes infinitely small as x continues to approach minus one. That is the end of the first segment.

There is an inifinite discontinuity at x equals minus one where the y-value is undefined.

The second segment begins when x is larger than but very close to minus one and y-value is very small. As it moves to the right, the graph increases steeply at first until x is close to zero, then it increases slowly until it reaches the point x is close to one and y is close to one. That is the end of the second segment.

There is a jump discontinuity at x equals one where the y-value jumps from one to three.

The shape of the third segment is a straignt line with a slope of negative one. It begins at x equals one and y equals three. As it moves to the right, the graph decreases. There is a removable discontinuity at x equals four where the y-value becomes two, instead of zero, at the point. The graph continues to decrease until x equals five and y equals minus one. That is the end of the third segment.

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