For the signum function (f(x)=\operatorname{sgn}(2-x)), what is the graph value for (x>2)?

Correct answer: ( -1 )

The direct answer is option A, -1. The signum function returns 1 when its input is positive, 0 when its input is zero, and -1 when its input is negative. If x>2, subtracting x from 2 gives 2-x<0. Therefore sgn(2-x)=-1, so the graph value is -1. Option A is correct. Option B, 0, would occur only when 2-x=0, which means x=2, not x>2. Option C, 1, would occur when 2-x>0, meaning x<2. Option D, 2, is the constant appearing inside the expression, not a possible signum output in this situation; signum outputs only -1, 0, or 1. The boundary x=2 is important: the value there is 0, while all values strictly to the right give -1. The supplied answer is consistent. Remember to determine the sign of the entire inside expression before applying signum.