Q. 23 - Calculus

Question

For each function f graphed in Exercises 23–26, describe the intervals on which f is continuous. For each discontinuity of f, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements. 

Step-by-Step Solution

Answer

The function is continuous on the interval $\left(-\infty ,2\right)\cup \left(2,\infty \right)$ and it has a removable discontinuity and there is not any one-sided continuity.

Step 1. Given Information.

The given graph is

Step 2. Describing the intervals on which f is continuous.

From the graph, we can depict that the graph is continuous on the interval $\left(-\infty ,2\right)\cup \left(2,\infty \right).$

Step 3. Describe the type of discontinuity and any one-sided continuity.

From the graph, we can depict that it has removable discontinuity because $\underset{x\to 2}{\lim }f\left(x\right)$ exists but it is not equal to $f\left(2\right).$

The graph is neither left continuous nor right continuous at $x=2.$