xLet g(x) =

x if x < 1 2 if x = 1 2 − x2 if 1 < x ≤ 2 x − 3 if x > 2 . (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) (i) lim x→1− g(x) (ii) lim x→1 g(x) (iii) g(1) (iv) lim x→2− g(x) (v) lim x→2+ g(x) (vi) lim x→2 g(x) (b) Sketch the graph of g.

The x y coordinate plane is given. A function comprised of two lines, one curve, and one point is on the graph. The point occurs at (1, 2). The first line enters the window in the third quadrant, goes up and right, passes through the origin, and ends at the open point (1, 1). The curve begins at the open point (1, 1), goes down and right becoming more steep, and ends at the closed point (2, −2). The second line begins at the open point (2, 1), goes down and right, crosses the x-axis at x = 3, and exits the window in the fourth quadrant.

The x y coordinate plane is given. A function comprised of two lines and one point is on the graph. The point occurs at (1, 2). The first line enters the window in the third quadrant, goes up and right, passes through the origin, and ends at the open point (1, 1). The second line begins at the open point (1, −2), goes up and right, crosses the x-axis at x = 3, and exits the window in the first quadrant.

The x y coordinate plane is given. A function comprised of two lines and one curve is on the graph. The first line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 1, and ends at the open point (1, 1). The curve begins at the open point (1, 1), goes down and right becoming more steep, and ends at the closed point (2, −2). The second line begins at the open point (2, −1), goes up and right, crosses the x-axis at x = 3, and exits the window in the first quadrant.

The x y coordinate plane is given. A function comprised of two lines, one curve, and one point is on the graph. The point occurs at (1, 2). The first line enters the window in the third quadrant, goes up and right, passes through the origin, and ends at the open point (1, 1). The curve begins at the open point (1, 1), goes down and right becoming more steep, and ends at the closed point (2, −2). The second line begins at the open point (2, −1), goes up and right, crosses the x-axis at x = 3, and exits the window in the first quadrant.

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