Q. 24 - 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 f is not continuous because the graph is not joined at any point. It has jump discontinuity and the function is left continuous at $x=-1.$

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 function is not continuous because it is not joined at any point.

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

From the graph, we can depict that it has jump discontinuity because $\underset{x\to c^{-}}{\lim }f\left(x\right) \mathrm{and} \underset{\mathrm{x}\to {\mathrm{c}}^{+}}{\lim }\mathrm{f}\left(\mathrm{x}\right)$ both exist but are not equal.

The function is left continuous at $x=-1.$