Similarity transformations are geometric transformations that preserve the shape of an object, but may change its size and orientation. They are a combination of a dilation, a rotation, and a reflection.
Dilation: A dilation scales an object by a factor of k, where k is a positive number. This means that every point in the object is moved farther away from the origin by a factor of k.
Rotation: A rotation rotates an object about a fixed point by an angle of θ. This means that every point in the object is moved to a new location that is θ degrees away from its original location.
Reflection: A reflection reflects an object across a line or plane. This means that every point in the object is moved to a new location that is the same distance away from the line or plane, but on the opposite side.
The image you sent shows a graph of a function f(x, y, z) with variables f(x, y, z), g(x, y, z), and h(x, y, z), and its image after the similarity transformation. The similarity transformation in this case is a dilation by a factor of 3/4 followed by a reflection in the x-axis.