The transformation from \(y = f(x)\) to \(y = f\left(\frac{1}{2}x\right)\) involves a horizontal stretch. Specifically, it is a stretch by a factor of 2 in the x-direction, as the x-values are effectively halved, making the graph wider.

The transformation from \(y = f(x)\) to \(y = 1 + f(x)\) involves a vertical translation. Specifically, it is a translation of 1 unit upwards in the y-direction, as 1 is added to the function value.

Therefore, the two transformations are: a stretch by a factor of 2 in the x-direction and a translation of 1 unit in the y-direction.