Plotting points and functions in one graphic

I have this plot:

Plot[{0 x, -x, x, -Sqrt[2 - x^2], Sqrt[2 - x^2]}, {x, -3, 3},
PlotStyle -> {Purple}] Now I want to do the following. I want to plot the points: $(-1,0),(1,0),(0,0),(x,0),(1, \pm 1),(1,\pm \frac{1}{\sqrt 3}),(0, \pm \frac{2}{\sqrt 3}),(0, \pm \sqrt 2)$ in this graphic. I'm able to plot points using Graphics[Point[{x, y}]but I would like to plot those point in the same graphic. This is probably really easy, but I can't find it in the documentation.

• Look Epilog in help. – BoLe May 15 '13 at 18:17
• just Show[ Plot[..] , Graphics[..] ] – george2079 May 15 '13 at 18:20
• Aah thanks ! got it – Kasper May 15 '13 at 18:29
• In the same vein as @george's suggestion: you could use Show[] to display the output of Plot[] and ListPlot[] together. – J. M. will be back soon May 15 '13 at 18:30

Thanks to george2079 I was able to get what I needed:

Data = {{-1, 0}, {1, 0}, {0, 0}, {1, 1}, {1, -1}, {1,
1/Sqrt}, {1, -1/Sqrt}, {0, 2/Sqrt}, {0, -2/Sqrt}, {0,
Sqrt}, {0, -Sqrt}}
Show[Plot[{0 x, -x, x, -Sqrt[2 - x^2], Sqrt[2 - x^2]}, {x, -3, 3},
PlotStyle -> {Purple}], Plot[0 x, {x, -3, 3}, PlotStyle -> {Blue}],
Graphics[{PointSize[Medium], Blue, Point[Data]}]] For fun, let's describe the ellipse--which is actually a circle--in polar coordinates and specify the points more simply as complex numbers rather than pairs of reals. And then use David Park's Presentations add-on (http://home.comcast.net/~djmpark/DrawGraphicsPage.html) in order to draw the whole thing--without having to use PlotStyle, Graphics, or Show (at least, not overtly):

pts = {1, 1 + I, 1 + I/Sqrt, 2 I/Sqrt};
pts = Join[{0}, pts, Conjugate[pts]];
Draw2D[{
Thick, Purple, PolarDraw[Sqrt, {t, 0, 2 Pi}],
Thickness[0.0035], Draw[{-x, x}, {x, -3, 3}],
Black, PointSize[Large], ComplexPoint /@ pts
},
Axes -> True, PlotRange -> 3] 