For the function f(x)=sgn(x), what is the value of f(x) when x<0?

Correct answer: −1

The governing concept is the signum function, which records whether its input is positive, zero, or negative. Its standard definition is sgn(x)=1 when x>0, sgn(x)=0 when x=0, and sgn(x)=−1 when x<0. Because the question gives x<0, the input is negative and the output must be −1. Therefore option C is correct. Option A belongs to the positive case x>0, while option B belongs only to the zero case x=0. Option D, x², is not a value assigned by the signum definition; it describes a different function and would also vary with x. The answer depends only on the sign of x, not on its magnitude, so every negative input produces the same value −1.