For the limit as x goes to 0 from the positive side you use the first branch of the function, since its domain is x > 0.

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 exists)

(limit equal to function value, so the graph, when you draw it, is filled)

Good luck!!