Show graphically a plotted curve and a point {0, -1} together?

Questions
1

The following notebook script can show 7 points on a plotted graph of Plot[x^2+1,{x,-3,2}]，but fails to show the point {0, -1} on the graph.
How can I show the point {0,-1} on the graph, too?

PlotPx = Plot[x^2 + 1, {x, -3, 2}];
PointSet = {{-3, 9}, {-2.5, 5.75}, {-2, 4}, {3, 9}, {-1, 2}, {-0.5, 
    1.75}, {0, -1}, {0, 2}, {1, 4}, {2, 8}};
PointMap = Map[Point, PointSet];
Show[PlotPx, Graphics[{PointSize[0.01], PointMap}], 
 AspectRatio -> Automatic, Axes -> True,
 AxesLabel -> {x, "y=P(x)"}]
2

I believe that I remember that Show takes the PlotRange from the first argument. So force the PlotRange to include your all your points

PlotPx = Plot[x^2 + 1, {x, -3, 2},PlotRange->{-1.5,6}];

And that includes your Point{{0,-1}]

There are almost always more than one way of doing anything with Mathematica..

3

Another way is to specify PlotRange -> All as an option to Show

Show[
 	PlotPx, Graphics[{PointSize[0.01], PointMap}],
 	AspectRatio -> Automatic, Axes -> True, AxesLabel -> {x, "y=P(x)"},
 	PlotRange -> All
 ]
4

You can also use Epilog[]:

Plot[x^2 + 1, {x, -3, 2}, Epilog -> Map[Point, data]]

Regards

Neil

5

Dear Mr. Neil Singer：I thank you very much for your quick answer to my elementary question. Your suggestion greatly helped me come out of the quagmire I have been struggling with the problem for more tna three days!

I know only little about the “Epilog”, but will spend some time to learn that.

Thank you very much again!

Sincerely, Hiroshi Matsumura (June 26, 2020)

6

Dear Mr. Hans Milton:
I am very greatful to your quick answer to my elementary question.
At last I could find a way out of the quagmire I have been struggling with the problem for more than three days!

Thank you very much again!

Sincerely, Hiroshi Matsumura (June 26, 2020)

7

Dear Mr. Bill Nelson:
Your instruction worked fine, and solved my problem which I have been struggling with for three days!
I am very grateful to your quick response to my elementary question.
Thank you very much again!

Sincerely, Hiroshi Matsumura (June 26, 2020)