Which graph represents the piece wise-defined function? y={−x+3   if  x< 12x−4   if  x≥1

For the interval (-∞, 1), put x = 0.5, then y = - 0.5 + 3 = 2.5.

Therefore, (0.5, 2.5) is a point on y = -x + 3.

Put x = - 1, then y = -(-1) + 3 = 1 + 3 = 4.

Therefore, (-1, 4) is another point on y = -x + 3.

Joining (0.5, 2.5) and (-1, 4), we get the graph of the line y = -x + 3.

For the interval [1, ∞), put x = 1, then y = 2(1) - 4 = -2.

Therefore, (1, -2) is a point on y = 2x - 4.

Put x = 2, then y = 2(2) - 4 = 4 - 4 = 0.

Therefore, (2, 0) is another point on y = 2x - 4.

Joining (1, -2) and (2, 0), we get the graph of the line y = 2x - 4.