By analyzing the graph we will see that the limit that does not exist is the last one.
How to analyze the graph of the function?
Well, the first thing we can see here is that this is a piecewise function, and it has a jump at x = 2
We can also see that the domain goes from -6 to 8.
Now we want to see which one of the given limits does not exist, remember that a limit is a tendency to a given value as x tends to a value.
With that in mind, and by reading the graph, we can see that the two limits (from left and right) for x → 2 do exist (there is a jump there, but we can approach that limit from both sides).
That is not the case for the limits of x → -6
As the domain starts in x = -6, the limit from the right (the one with the plus sign) does exist (because it approaches the value -6 from larger values, that are on the domain), but the other limit does not, as it would approach to -6 from smaller values, and these are not in the domain.
So the correct option is the fourth one.
If you want to learn more about limits, you can read:
https://brainly.com/question/12383180
