Signum Function

The signum function outputs -1 for negative inputs, 0 at zero, and 1 for positive inputs, capturing only the sign of its argument, a definition used in JEE Advanced limit and graph questions. Evaluate each term: sgn(-5) = -1 because -5 is negative. sgn(0) = 0 by definition at the origin. sgn(7) = 1 because 7 is positive. sgn(-0.001) = -1 because the argument, though tiny, is still negative. Adding these gives -1 + 0 + 1 + (-1) = -1. Option 0 wrongly treats the small term sgn(-0.001) as 0 as if -0.001 were negligible. Option 1 mishandles the small negative term as positive. Option 2 ignores both negative contributions. Hence the sum equals -1. Plausibility check: signum depends only on sign, not magnitude, so -0.001 behaves exactly like any negative number, and the total counts one positive against two negatives and one zero, giving a net of -1.