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Quiz 1

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 two.

Answer

The graph has a jump discontinuity at x equals two.

Explanation

The graph consists of two segments.

The shape of the first segment is a parabola, concave down (i.e. similar to upside-down U-shape). It begins at the point of x equals minus five and y is about minus three. As it moves to the right, the graph increases slowly till it reaches the maximum at x equals zero and y equals two. Then the graph changes direction to go down until x equals two and y is about one.

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

The second segment begins at x is greater than but not equal to two and y is greate than but not equal to minus 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 one.

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