Choose the most appropriate equation for the function drawn as thick line, in the plot below. [Plot shows a piecewise curve: for y < 0 the function z equals twice the negative y value (V-shape reflected), for y >= 0 the function z is 0] A. z = y - |y| B. z = -(y - |y|) C. z = y + |y| D. z = -(y + |y|)

GATE 2015 · General Aptitude · Functions · medium

Answer: z = -(y - |y|)

1. Test Option A: z = y - |y| at y = -2: y = -2: z = -2 - |-2| = -2 - 2 = -4 (negative). Graph shows z > 0 for y < 0. Eliminate A.
2. Test Option B: z = -(y - |y|) at y = -2: y = -2: z = -(-2 - 2) = -(-4) = 4 (positive). Graph shows z > 0 for y < 0. Matches!
3. Verify Options C and D are eliminated: C at y=2: z = 2 + 2 = 4 (not 0 for y>0, eliminated). D at y=2: z = -(4) = -4 (eliminated).
4. Confirm: z = -(y - |y|) general form: For y >= 0: |y| = y, so z = y - y = 0. For y < 0: |y| = -y, so z = -y - y = -2y > 0. Perfectly matches the graph.