Q. 26 - 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 graph is continuous on the interval $\left(-\infty ,-1\right)\cup \left(-1,2\right)\cup \left(2,\infty \right)$ and it has a jump discontinuity and the function is right continuous at $x=2.$

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 graph is continuous on the interval $\left(-\infty ,-1\right)\cup \left(-1,2\right)\cup \left(2,\infty \right).$

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

From the graph, we can depict that it has a jump discontinuity. The function is right continuous at $x=2.$