${\displaystyle k(x)=\left\{{\begin{matrix}1,&{\mbox{if }}x>0\\-1,&{\mbox{if }}x\leq 0\end{matrix}}\right.}$,

similar to the signum function. Created using the following Sage code:

def k(x):        
    if x > 0:                                        
        return 1
    return -1

plot(k, xmax=2, xmin=-2, ymax=2, ymin=-2, exclude=[0], thickness=2.5) + 
point([0, -1], size=80, zorder=4) + point([0, 1], size=80, faceted=True, rgbcolor='white', zorder=4)