which of the following accurately lists all of the discontinuities for the function graphed below?\n\ngraph…

which of the following accurately lists all of the discontinuities for the function graphed below?\n\ngraph of a function\n\no jump discontinuity at x = 0; point discontinuity at x = 8\no jump discontinuity at x = 0; point discontinuities at x = -2 and x = 8\no jump discontinuities at x = 0 and x = 8; point discontinuity at x = -2\no jump discontinuity at x = 0; point discontinuities at x = -2, x = 3 and x = 8

which of the following accurately lists all of the discontinuities for the function graphed below?\n\ngraph of a function\n\no jump discontinuity at x = 0; point discontinuity at x = 8\no jump discontinuity at x = 0; point discontinuities at x = -2 and x = 8\no jump discontinuities at x = 0 and x = 8; point discontinuity at x = -2\no jump discontinuity at x = 0; point discontinuities at x = -2, x = 3 and x = 8

Answer

Explanation:

Step1: Identify jump - discontinuity

At (x = 0), the left - hand limit and the right - hand limit of the function are different. The function has a break in the graph where the value of the function jumps from one value to another. So, there is a jump discontinuity at (x=0).

Step2: Identify point - discontinuities

A point discontinuity (removable discontinuity) occurs when there is a hole in the graph. At (x=- 2), the graph has a hole, so there is a point discontinuity. At (x = 8), the graph has a hole, so there is a point discontinuity. At (x = 3), the graph is continuous.

Answer:

jump discontinuity at (x = 0); point discontinuities at (x=-2) and (x = 8)