**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.

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