Question

watch the video and then solve the problem given below. click here to watch the video. determine the intervals of the domain over which the function shown to the right is continuous. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function is continuous over the interval type your answer in interval notation. b. the function is not continuous.

Explanation:

Step1: Recall continuity definition

A function is continuous on an interval if there are no breaks, jumps, or holes in its graph on that interval.

Step2: Analyze the given graph

The graph of the function is a straight - line with a hole at \(x = - 2\).

Step3: Determine the intervals of continuity

The function is continuous everywhere except at \(x=-2\). So the intervals of continuity are \((-\infty,-2)\cup(-2,\infty)\).

Answer:

A. The function is continuous over the interval \((-\infty,-2)\cup(-2,\infty)\)