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Chapter 1: Q. 11 (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�0-f(x)=-1,limx鈫�0+f(x)=1,f(0)=0.

Short Answer

Expert verified

The type of discontinuity is a jump discontinuity and there is not any one-sided continuity.

The possible graph of fis

Step by step solution

01

Step 1. Given Information. 

The given function islimx鈫�0-f(x)=-1,limx鈫�0+f(x)=1,f(0)=0.

02

Step 2. Describing the discontinuity. 

From the function, we can depict that limx鈫�0-f(x)=-1andlimx鈫�0+f(x)=1both exist but are not equal tof(0)=0.

Thus,f(x)has a jump discontinuity atx=0.

03

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

There is not any one-sided continuity at x=0because limx鈫�0-鈮�f(0)andlimx鈫�0+鈮�f(0).

04

Step 4. Graph of f.

The graph of fis

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