Question

Which is the graph of g(x)?

g(x) = StartLayout Enlarged left-brace 1st row 1st column 3, 2nd column x less-than negative 2 2nd row 1st column negative StartFraction x Over 2 EndFraction + 2, 2nd column negative 2 less-than-or-equal-to x less-than 2 3rd row 1st column 2 x minus 3, 2nd column x greater-than-or-equal-to 2 EndLayout

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 5, 3) and continues horizontally to (negative 2, 3). The second line has a closed circle at (negative 2, 2) and goes down to a closed circle at (2, 0). The third line has a closed circle at (2, 1) and goes up through (3, 3).

On a coordinate plane, a piecewise function has 3 connecting lines. The first line starts at (negative 5, 3) and goes horizontally to (negative 2, 3). The second line goes from (negative 2, 3) down to (2, negative 5). The third line starts at (2, negative 5) and goes up to (5, 1).

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 5, 3) and continues horizontally to (negative 2, 3). The second line has a closed circle at (negative 2, 2) and goes down to a closed circle at (2, 0). The third line has a closed circle at (2, negative 3) and goes up through (4, 1).

On a coordinate plane, a piecewise function has 3 connecting lines. The first line starts at (negative 5, 3) and goes horizontally to (negative 2, 3). The second line goes from (negative 2, 3) down to (2, 1). The third line starts at (2, 1) and goes up through (3, 3).

Answer 1

The fourth graph.

Reason: For x < −2 g(x)=3 so the graph is horizontal at y=3 up to x=−2. For −2 ≤ x < 2 g(x)=−x/2+2, which gives g(−2)=3 and g(2)=1 and slope −1/2, so the middle segment runs from (−2,3) down to (2,1). For x ≥ 2 g(x)=2x−3, which starts at (2,1) and passes through (3,3). That matches the fourth description.