Mathematics

Mathematics

Problem

The function gg is defined as g(x)={−1,x<00,x=01,x>0.g(x)=\begin{cases}-1, & x<0\\0, & x=0\\1, & x>0\end{cases}. To which standard family does gg belong? a) Modulus function b) Greatest–integer function c) Signum function d) Heaviside step function
Intuitive explanation

The function gg is the sign function, which classifies any input by its position relative to zero. Rather than measuring a quantity, it extracts just the sign—negative, zero, or positive—making it a fundamental building block in mathematics for conditional logic and piecewise definitions. Recognizing this standard function helps you understand how to work with it in proofs, limits, and more complex constructions.

Intuitive explanation

The function gg is the sign function, which classifies any input by its position relative to zero. Rather than measuring a quantity, it extracts just the sign—negative, zero, or positive—making it a fundamental building block in mathematics for conditional logic and piecewise definitions. Recognizing this standard function helps you understand how to work with it in proofs, limits, and more complex constructions.

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