What piecewise function f(x) has opposite expressions

We are given a piece-wise function f(x) as:

  f(x)=  2x-1  when x<0

            0 when  x=0

and     -2x+1   when x>0

we have a graph of the function as a straight line with positive slope, this means that the line is increasing in the interval (-∞,0)

and also at (0,-1) there will be a open circle

since when x→0- then f(0)→2×0-1= -1

The value of the function is 0

Hence, we get the point (0,0)

we get the graph as a decreasing line since the slope of the line is negative i.e. -2.

and the graph starts with open circle at (0,1)

since x→0+ we have:  f(0)→1

            The correct graph is attached to the answer.

yes. we do proportions in probabilities.