How does one plot piecewise functions, with the ability to plot individual points along with open points to clearly show how values are defined at discontinuities?
Example:
with the dashed vertical line omitted.
2 Answers
$\begingroup$
$\endgroup$
Something to get you started
Plot[HeavisideTheta[x], {x, -1, 1},
ExclusionsStyle -> None,
Epilog -> {
{
FaceForm[None],
EdgeForm[ColorData[97][1]],
Disk[{0, 1}, .025]
},
{
ColorData[97][1],
Disk[{0, .5}, .025]
},
{
FaceForm[None],
EdgeForm[ColorData[97][1]],
Disk[{0, 0}, .025]
}
},
Frame -> True,
Axes -> False,
ImageSize -> 500
]
$\begingroup$
$\endgroup$
I don't find the elegant way to un-clipped or un-filled the point,so I have to use White.
Clear[f];
f[x_] := Piecewise[{{1/2, x == 0}}, HeavisideTheta[x]];
Plot[f[x], {x, -5, 5},
Epilog -> {Style[Point[{0, 1/2}], PointSize[Large], Blue],
Style[Point[{0, 1}], PointSize[Large], Green],
Style[Point[{0, 1}], PointSize[Medium], White],
Style[Point[{0, 0}], PointSize[Large], Cyan],
Style[Point[{0, 0}], PointSize[Medium], White]}, Axes -> False,
Frame -> True]
HeavisideThetafunction is not a usual function, but a distribution (i.e. a certain functional). $\endgroup$HeavisideTheta. Hope I am clear. $\endgroup$