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Chapter 14: Q. 30 (page 889)

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Is f continuous at 2?

Short Answer

Expert verified

The answer is no. The function is not continuous at 2.

Step by step solution

01

Step. 1 How to check continuity? 

For a function to be continuous its LHL = RHL = f(c) at the pointx=c.

02

Step. 2 Calculating LHL, RHL and f(c).

Firstly we calculate f(2)which is equal to 3 as given in the graph.

Now, we calculate LHL which is,

limx鈫�2-f(x)=1.

Finally we see RHL which is,

limx鈫�2+f(x)=-4.

From here we can see that LHL鈮�RHL鈮�f(2)

So, the conditions to check continuity fails. That's why, the function is not continuous at x=2.

And from the graph itself we can clearly see that we have to pick our pencil up the paper when we move through x=2which is also a method to check whether the function is continuous or not.

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