A marble starts from rest down the inside of a bowl and rolls without slipping. at the bottom the surface changes to a frictionless surface. The marble then moves up the other side to a certain height. Is this height higher, lower, or the same as the height from which the marble started

The height will be lower.

Explanation:

The marble starts from a certain height with some potential energy and as it rolls down the bowl, the potential energy that it has is converted into kinetic energy as movement but it also loses some of it's total energy to the friction force between the marble and the surface of the bowl therefore when the marble reaches the bottom of the bowl, the total energy that it has is less than the energy it began with.

Even though the surface upwards is frictionless, the loss of energy from the downwards motion will result in the marble reaching a lower heigth than its first height when it began moving.

I hope this answer helps.

The height will be the same.

Explanation:

At the top, the marble is at rest and the only energy it has is potential energy. As long as the marble is at the top of the container, the potential energy will be the same at any point and since it is at rest there will be no loss due to friction. It can be said that the height at which the marble will be raised will be the same as well.