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Question: I am unsure how to graph the interpolated graph with the regular graph on the interval $[1,4]$. Not even the Show line works about even if I'm pretty sure it's written correctly.

Clear["Global`*"]

f[x_] = x e^-x - 1

f[1];

f[2];

f[3];

f[4];

XY = {{1, -1 + 1/e}, {2, -1 + 2/e^2}, {3, -1 + 3/e^3}, {4, -1 + 4/
     e^4}};

p4[x_] = Fit[XY, {1, x, x^2, x^3, x^4}, x]

dots = ListPlot[XY, PlotStyle -> {PointSize[0.02]}];

gr5 = Plot[{f[x], p4[x]}, {x, -0.6, 2.1}, PlotStyle -> {Red, Green}];

Show[gr5, dots, PlotRange -> {{0, 1.2}, {0.0, 1.15}}]
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Here you go!

f[x_] := x*Exp[-x - 1]; 
XY = {{1, -1 + 1/Exp[1]}, {2, -1 + 2/Exp[2]}, {3, -1 + 3/Exp[3]}, {4, -1 + 4/Exp[4]}}; 
p4 = Fit[XY, {1, x, x^2, x^3, x^4}, x]; 
dots = ListPlot[XY, PlotStyle -> {PointSize[0.02]}]
gr5 = Plot[{f[x], p4}, {x, -0.6, 2.1}, PlotStyle -> {Red, Green}]
Show[gr5, dots, PlotRange -> {{0, 1.2}, {0., 1.15}}]

enter image description here

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  • $\begingroup$ OHH yes now I see why my code was incomplete.Thank you so much! Although, now I think there must be a mistake with the code itself for I assumed the dots would be on the interpolated functions line, since isn't that the whole point of interpolation hm.. $\endgroup$ – Sherien Hassan Oct 20 at 21:21

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