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Quiz 4

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. State the x-values at which the graph has a removable discontinuity.

Answer

The graph has two removable discontinuities. The first is at x equals minus three where the y-value is undefined, so you will not hear any sound at the point. The second is at x equals four where the y-value becomes larger, so you will hear higher pitch at the point.

There is also a jump discontinuity in this graph at x equals minus two, which is not asked in this question.

Explanation

The graph consists of two segments.

The shape of the first segment is a straight line with a slope of minus two. It begins at x equals minus five and y equals two. As it moves to right, the graph begins to decreas and there is a removable discontinuity at x equals minus three where the y-value is undefined. The first segment ends at x is less than minus two and y is less than four.

There is a jump discontinuity at x equals minus two. The y-value jumps from minus four to about minus two.

The shape of the second segment is a wave that oscillates betweel minus two and two. The graph begins x equals minus two and y is larger than minus two. As it moves to the right, the graph initially decreases, then increases until it reaches x is close to two and y is close to two, then decreases again. There is a removable discontinuity at x equals four where the y-value becomes two at the point.

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