After the united states purchased the louisiana territory, america’s western boundary shifted to the which is a(n) boundary.
a.

mississippi river . . visible
b.

mississippi river . . political
c.

rocky mountains . . physical
d.

rocky mountains . . imaginary

It shifted to the Rocky mountains, so either C or D.

Now, the border was actually not  defined at the time, and it was disputed, and it was regulated only later, so I think that the best answer is D - "imaginary", although Rocky mountains are ale a physical border.

After the United States purchased the Louisiana Territory, America’s western boundary shifted to the Mississippi river, which is a physical boundary.

Afine-grained igneous rock forms as a result of slow cooling.