Mathematics

The sign function $\mathrm{sgn}(x)$ only takes three discrete values—it jumps between $-1$, $0$, and $1$ depending on whether $x$ is negative, zero, or positive. Since $f(x)$ is just a linear transformation of $\mathrm{sgn}(x)$, the range will be a finite set of three specific output values. Plug in each possible value of the sign function to see what outputs you get.

The sign function $\mathrm{sgn}(x)$ only takes three discrete values—it jumps between $-1$, $0$, and $1$ depending on whether $x$ is negative, zero, or positive. Since $f(x)$ is just a linear transformation of $\mathrm{sgn}(x)$, the range will be a finite set of three specific output values. Plug in each possible value of the sign function to see what outputs you get.