a. Is g(s) continuous in the open interval (-1, 2).
Observe the graph. We see g(x) has no gap in the open interval (-1, 2), therefore, it is continuous in the given interval.

b. Is g(x) continuous from the right at x = -1? Is limit_x→-1⁺ = g(-1)?
To see the function being continuous or not we have,
limit_x→-1⁺ g(x) = (-1-2+2) = -1
The limit exists at x = -1.
g(-1) = -1
limit_x→-1⁺ g(x) = g(-1)
So it is continuous.

c. Is g(x) continuous from the left at x = 2?
Is lim_x→2^–g(x) = g(2)
Now, g(2) = -4+4+2 = 2
lim_x→2^–g(x) = lim_x→2^– -4+4+2 = 2
So g(2) = lim_x→2^–g(x)
Therefore, g(x) is continuous at x = 2 and g(x) = g(2).

d. Is g(x) continuous on the closed interval [-1, 2]?
Yes. see the fig.