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Quiz 3

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 jump discontinuity.

Answer

The graph has two jump discontinuities at x equals minus one and x equals two.

Explanation

The graph consists of three segments.

The first segment begins at x equals minus five and y is about minus one. Its shape is a parabola, concave down (i.e. similar to upside-down U-shape). As it moves to the right, the graph increases till it reaches the point of x equals minus three and y equals three. Then it decreases till x is close to and less than minus one and y is close to and less than minus one.

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

The second segment begins at x equals minus one and y is about three. Its shape is a parabola, concave down. As it moves to the right, the graph increases at first till it reaches the point of x equals zero and y equals three. Then it decreases till x is close to and less than two one and y is about two.

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

The third segment begins at x equals two and y equals minus one. Its shape is a parabola, concave up. As it moves to the right, the graph decreases at first it reaches the point of x equals minus three and y equals minus three. Then it increases till x equals five and y equals five.

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