Long and cross profiles of a river

Long profile of a river
The steep reduction in height near the source gives way to a more gradual reduction further downstream, giving a typical concave profile. The river has much potential energy near the source due to the steep drop. Later on, this is replaced by energy from a large volume of water. However, such a perfect long profile is rare. This is due to land being uplifted, sea-level changing and bands of hard and soft rock crossing the path of the river.
Cross profile and long profile in more detail
You may be asked to describe how and why it changes downstream. It is related to the amount of energy a river has. As it moves downstream it loses energy as the gradient becomes less steep. The valley widens as the river changes from vertical erosion to lateral erosion as the river has less energy.