You can choose among different approaches. One is to combine different formulas for the negative and positive using Piecewise
:
f[x_] = Piecewise[{{1 - x, x > 0}, {x - 1, x < 0}}];
Plot[f[x], {x, -2, 2}, Epilog -> {PointSize[Large], Point[{0, 1/2}]}]
Another way is to combine separate plots with Show
:
Show[Plot[1 - x, {x, 0, 2}], Plot[x - 1, {x, -2, 0}],
Graphics[{PointSize[Large], Point[{0, 1/2}]}], PlotRange -> All]
An isolated point of the graph requires a separate treatment, as Plot
is meant for curves only.