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Chapter 14: Q. 27 (page 889)

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

Is f continuous at -6?

Short Answer

Expert verified

The answer is no. The function is not continuous at -6.

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).

As we can see that x=-6doesn't exist even in the domain of f(x).

So, f(-6) doesn't exist. Therefore, we don't need to calculate LHL and RHL from here itself we can conclude that f(x) is not continuous at x=-6.

And from the graph itself we can clearly see that we have to pick our pencil up the paper when we move through x=-6which is also a method to check whether the function is continuous or not.

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