how to plot vertical lines

savecancel

If P and Q are plots then you may display them together via P+Q.

For the vertical line you may use implicit_plot or just draw it manually via line.

var('x,y')
# plot line x=3
P = implicit_plot(x==3,(x,2,4),(y,-1,5))

# manualy draw line x=5
Q = line([(5,-1),(5,5)])

# display P and Q together.
(P+Q).show()

Guess plotting y=x^3 can be left as an exercise ;-)

Hint.