Question

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 (-∞, - 4)∪(- 4,∞). (type your answer in interval notation.) b. the function is not continuous.

Explanation:

Step1: Recall continuity definition

A function is continuous at a point if the limit as x approaches that point exists and is equal to the function - value at that point. Visually, a continuous function has no breaks, jumps, or holes.

Step2: Analyze the graph

Looking at the graph, there is a break in the function at \(x = - 4\). The function is composed of two linear - like parts that are not connected at \(x=-4\). The function is continuous everywhere else.

Answer:

A. The function is continuous over the interval \((-\infty,-4)\cup(-4,\infty)\)