Question

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

Is f continuous at -6?

Short answer

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

Step-by-step solution

Step. 1 How to check continuity?

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

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

As we can see that $x=-6$doesn'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 $x=-6$which is also a method to check whether the function is continuous or not.