Use the given graph to determine the limit, if it exists. find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.

We can see from the graph, as the value of x approaches 2 from the left hand side i.e. the negative side, the value of the function approaches 4.

As the value of x approaches 2 from the positive side i.e. the right hand side, the value of function approaches -4

Since the Right hand limit and the Left hand limit as x approaches 2 are not the same, the limit does not exist at x = 2