Graphing with Mathematica

Basic 2D plotting

So we want to graph y=f(x) on an xy-plane, and go through many options available

f[x_] = 3x^2+3x-1;
g[x_] = 2x^2+2x-1;

Plot[g[x],{x,-3,3}]

Plot[g[x],{x,-3,3},PlotStyle->{Blue, Thickness[0.004]}]

Plot[g[x],{x,-3,3},PlotStyle->{Blue, Thickness[0.004]}, PlotLegends->"g(x)"]

Plot[{f[x],g[x]},{x,-3,3},PlotStyle->{{Blue, Thickness[0.004]},{Red,Dashed,Thickness[0.006]}}, PlotLegends->{"f(x)","g(x)"}]

FunctionPlot = Plot[{f[x],g[x]},{x,-3,3},PlotStyle->{{Blue, Thickness[0.004]},{Red,Dashed,Thickness[0.006]}}, PlotLegends->{"f(x)","g(x)"},PlotRange->{{-1.5,0.5},{-2.0,0.5}}]

ShadedPlot = RegionPlot[g[x]>y && y> f[x],{x,-2,0.5},{y,-2,0},PlotPoints->100,Axes->True,PlotRange->{{-1.5,0.5},{-2.0,0.5}},PlotStyle->LightOrange,BoundaryStyle->None]

Show[FunctionPlot,ShadedPlot, AxesLabel->{"x","y"}]

ShadedPlot2 = RegionPlot[g[x]>y && y> f[x]&&x>-1/2,{x,-2,0.5},{y,-2,0},PlotPoints->100,Axes->True,PlotRange->{{-1.5,0.5},{-2.0,0.5}},PlotStyle->LightMagenta,BoundaryStyle->None]

Show[FunctionPlot,ShadedPlot,ShadedPlot2, AxesLabel->{"x","y"}]

Plot