To evaluate the limit, write
and note that OR both go to 1 as x approaches 0.
So the limit becomes 6 + 0* 1 = 6
For the other limit use the third branch, which gives
You haven't shared the conditions this problem wants. I assume it's continuity, which means the limits from the left and right are equal to the function value.
So, two conditions:
(limit equal to function value, so the graph, when you draw it, is filled)