Short Answer

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.

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $(- \infty, 2) \cup (2, \infty) .$

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

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

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

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Calculus

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Short Answer

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

Step 1. Given Information.

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

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

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Calculus

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Short Answer

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

Step 1. Given Information.

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

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

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