Question

let f be the function below. you may click on the graph to make it larger. use help (intervals) to indicate where f is continuous. answer:

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 function is continuous on an interval if its graph can be drawn without lifting the pen.

Step2: Analyze the graph

Identify the breaks, jumps, or vertical asymptotes in the graph. From the graph, we can see that there are vertical - asymptote - like behavior and jump - discontinuities.

Step3: Determine continuous intervals

We look for the intervals where the function has no breaks. Let's assume the $x$ - values of the discontinuities are $x = a$ and $x = b$. The function is continuous on the intervals where there are no such disruptions.

Answer:

(Assuming the vertical asymptotes are at $x=- 1$ and $x = 1$) $(-\infty,-1)\cup(-1,1)\cup(1,\infty)$ (The actual intervals should be determined precisely based on the exact $x$ - values of the discontinuities in the given graph)