A limit of a function does not exist at a point x is the limit of f(x) approaching x to the left is different of the limit of f(x) approaching x to the right.
Using this concept, we find that the limit does not exist at c = -2.
Points we need to verify:
Points in which there are changes in the definition of the function, which are:
x = -4, -2, 2, 4
At x = -4
The definitions are bunched together, so the lateral limits are the same, and the limit exists.
At x = -2
As the function approaches x = -2 to the left(x < -2), its value is close to 4, so the limit is 4.
As the function approaches x = -2 to the right(x > -2), its value is close to 6, so the limit is 6.
Since the lateral limits are different, for c = 2, the limit does not exist, and this is the correct answer.
At x = 2
The lateral limits are the same, the only thing that changes is the definition of the function at x = 2, which does not affect the limit, which exists.
At x = 4
The definitions are bunched together, so the lateral limits are the same, and the limit exists.
For more on lateral limits, you can take a look at https://brainly.com/question/23405626
