Question

determine the largest open intervals of the domain over which the function is continuous. select the correct choice below and, if necessary, fill in the answer box within your choice. a. the function is not continuous over all real numbers, and the largest open interval(s) of the domain over which the function is continuous is/are (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is continuous everywhere. c. the function is not continuous anywhere.

Explanation:

Step1: Recall continuity definition

A function is continuous over an open - interval if there are no breaks, jumps, or holes in the graph of the function over that interval.

Step2: Analyze the given graph

Looking at the graph, we can see that the function has a vertical asymptote at \(x = 0\). The function is continuous for \(x<0\) and \(x > 0\).

Step3: Write the intervals

The function is continuous on the intervals \((-\infty,0)\) and \((0,\infty)\).

Answer:

A. The function is not continuous over all real numbers, and the largest open interval(s) of the domain over which the function is continuous is/are \((-\infty,0),(0,\infty)\)