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Chapter 1: Q. 9 (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�-1-f(x)=2,limx鈫�-1+f(x)=2,f(-1)=1.

Short Answer

Expert verified

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

The possible graph of f is

Step by step solution

01

Step 1. Given Information.

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

02

Step 2. Describing the discontinuity.

From the function, we can depict that limx鈫�-1exists but is not equal to f(-1).

Thus,f(x)has a removable discontinuity atx=-1.

03

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

There is not any one-sided continuity atx=cbecauselimx鈫�-1-鈮�f(-1)andlimx鈫�-1+鈮�f(-1).

04

Step 4. Graph of f.

The graph of fis

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