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Quiz 2

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. Detemine the type of discontinuity the graph has at x equals minus one and x qeuals two.

Answer

The graph has an infinite discontinuity at x equals minus one, and a jump discontinuity at x equals two.

Explanation

The graph consists of three segments.

The first segment begins at x equals minus five and y is negative and close to zero. As it moves to the right, the graph decreases slowly. Then it decreases steeply and the y-value becomes infinitely small as x continuies to approach minus one.

There is an infinite discontinuity at x equals minus one.

The second segment begins when x is close to minus one from the right side and y-value is very large. As it moves to the right, the graph decreases steeply. Then it decreases slowly and the y-value becomes close to zero. It ends when x is less than two.

At x equals two, there is a jump discontinuity and y jumps from about zero to two.

The third segment begins at x equals two and y equals two. Its shape is a straight line with a slope of one. As it moves to the right, the graphs increases until it reaches the point of x equals five and y equals five.

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