Matthew Ebert
Math 329 Pg 1019

Problem 14

Clear [g,f]
f[x_]:=x^2
g[x_]:=3x
Plot[{g[x],f[x]},{x,0,4}]
RegionPlot[y≤g[x]&&y≥f[x],{x,0,3},{y,0,9}]

Problem 16
Clear [f,g,x,y]
f[x_]:=x
g[x_]:=4
Plot[{g[x],f[x]},{x,0,4}]
RegionPlot[y≤g[x]&&y≥f[x],{x,0,4},{y,0,4}]

Problem 28
Clear [f,g,x,y,z]
z[x_,y_]:=x
RegionPlot3D[y<2-x&&y>x&&z>x,{x,0,1},{y,0,1},{z,0,1},PlotPoints->50,AxesLabel->{x,y,z}]

Problem 35
Clear [f,g,z,x,y]
f[x_,y_]:=1-x^2
g[x_,y_]:=x^2-1
z[x_,y_]:=2-x-y
h[x_,y_]:=10+2x+2y
RegionPlot3D[y<f[x,y]&&g[x,y]<y&&z>2-x-y&&z<10+2x+2y,{x,-1,1},{y,-1,1},{z,0,14},PlotPoints->50,AxesLabel->{x,y,z}]

Problem 48
Clear[f,g,z,x,y,h]
f[x_]:=ArcTan[x]
Plot[{f[x],y=Pi/4},{x,0,1}]
RegionPlot[y>=f[x]&&y<=Pi/4,{x,0,1},{y,0,1}]