Determine the domain and range of the piecewise function Dom

Determine the domain and range of the piecewise function. Domain [-1. 1]; Range (-2, 0] Domain [-1. 3]; Range [-2, 2] Domain [-2, 2]; Range [-1, 3] Domain [-2, 0]: Range [-1, 1]

Solution

The graph of the piecewise function is in the 3^rd, 4^th and 1^st quadrants. In the 3^rd quadrant, the input i.e. x variable moves between -1 and 0. In the 4^th quadrant, x varies between 0 and 1 and in the 1st quadrant, x varies between 1 and 3. Therefore, the domain of the piecewise function is [ -1, 3]

In the 3^rd quadrant, the output i.e. y variable moves between 0 and -2. In the 4^th quadrant, y varies between -2 and 0 and in the 1st quadrant, y varies between 0 and 2. Therefore, the range of the piecewise function is [ -2, 2]. Thus, the answer is B Domain: [ -1,3]; Range: [ -2, 2]