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Chapter 1: Q. 10 (page 119)

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�2-f(x)=2,limx鈫�2+f(x)=1,f(2)=1.

Short Answer

Expert verified

The type of discontinuity is a jump discontinuity and f(x)is right continuous at x=2.

The graph of f is

Step by step solution

01

Step 1. Given Information. 

The given function islimx鈫�2-f(x)=2,limx鈫�2+f(x)=1,f(2)=1.

02

Step 2. Describing the discontinuity. 

From the function, we can depict that limx鈫�2-f(x)=2andlimx鈫�2+f(x)=1both exist but are not equal to f(2)=1.

Thus, f(x)has a jump discontinuity atx=2.

03

Step 3. Describing one-sided continuity at x=c.

The f(x)is right continuous at x=2but not left continuous becauselimx鈫�2+f(x)=f(2).

04

Step 4. Graph of f.

The graph of fis

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