which of the following accurately lists all of the discontinuities for the function graphed below? jump…

which of the following accurately lists all of the discontinuities for the function graphed below? jump discontinuity at x = 0; point discontinuity at x = 8 jump discontinuity at x = 0; point discontinuities at x = -2 and x = 8 jump discontinuities at x = 0 and x = 8; point discontinuity at x = -2 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? jump discontinuity at x = 0; point discontinuity at x = 8 jump discontinuity at x = 0; point discontinuities at x = -2 and x = 8 jump discontinuities at x = 0 and x = 8; point discontinuity at x = -2 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 function has a jump - discontinuity. The left - hand limit and the right - hand limit of the function at (x = 0) exist but are not equal.

Step2: Identify point - discontinuities

At (x=-2), there is a hole in the graph, so it is a point discontinuity. At (x = 3), there is a hole in the graph, so it is a point discontinuity. At (x = 8), there is a hole in the graph, so it is a point discontinuity.

Answer:

jump discontinuity at (x = 0); point discontinuities at (x=-2,x = 3) and (x = 8)