#How would you plot the function y^3-x?
var('x','y')
plot3d(y^3-x,(x,0,3),(y,-1,1))

#Show how the function y^3-x and the function  x^2 are related by adding them in the same plot.
var('x''y')
S1=plot3d(y^3-x,(x,0,3),(y,-1,1))
S2=plot3d(x^2,(x,0,3),(y,-1,1),color='red')
show(S1+S2)

#How can you use the aspect ratio command to receive a different visualization of the height and width of the graph?
var('x','y')
plot3d(y^3-x,(x,0,3),(y,-1,1), aspect_ratio=[1,1,1])

# Can you plot polar coordinates in 3D?
︠ab25ac97-95e4-45a6-a548-56c4a54df4d3︠
# try plotting (rho,theta,phi)=(2,pi/4,2pi/3)
var('rho','theta','phi')
plot3d(2,pi/4,2pi/3)

# sage will not plot polar coordinates but you can name the variables whatever you want. However, they will always be shown as Cartesian points in plot3d. For example:
var('rho','phi')
f=(phi^3-rho)
S=plot3d(f,(rho,0,3),(phi,-1,1))
show(S)

# Show how sage can use 3d graphing to portray trigonometric functions.
var('x','y')
S1 = plot3d(sin(x), (x, 0, 2*pi),(y,0,2*pi),opacity=.3)
S2 = plot3d(cos(x),(x,0,2*pi),(y,0,2*pi),color='green',opacity=1)
S3 = plot3d(tan(x),(x,0,2*pi),(y,0,2*pi),color='yellow',opacity=.4)
show(S1+S2+S3)

#Here's another experiment
var('x', 'y')
z=9-1/4*(x**2+y**2)
plot3d(9-1/4*(x**2+y**2),(x,-6,6),(y,-6,6))