The absolute functions involve reflection.
If we start with f0(x)=x as the parent function, the first transformation is a right shift (as you said) of 2 units:
f1(x)=x-2, then a dilation (vertical stretch) by a factor of 2 gives us f2(x)=2(x-2). This increases the slope of the line.
The final transformation f3(x)=|2x-4| is a reflection in the line of symmetry x=2, where (2,0) is the x-intercept, giving the graph a V shape.
If g0(x)=x3 is the parent function, then g1(x)=2x3 is a vertical stretch.
To create a stretch in the horizontal and vertical directions we can investigate what we expect to happen. This is the normal parent function h0(x)=x3.
x: 0, 1, 2, 3, 4, 5
h0(x)=x3: 0, 1, 8, 27, 64, 125.
Let x=t3 and y=t3, where t is a parameter. But this just creates the line y=x with ordered pairs (0,0), (1,1), (8,8), (27,27), ... for t=0, 1, 2, 3, ... This is the only way I can think of which makes the coordinates depend on a variable cubed.
I'm not sure what you mean by stretching in two directions, because this would just be a change of scale. The shape of the graph remains the same, like a magnification. A circle or ellipse can be magnified or miniaturised by changing the length of the axes (or radii) in the context of the graph equation. A parabola can be widened or narrowed by changing the coefficient of the quadratic variable. y=x3/a changes the shape of the cubic, making it wider but this is not the same as vertical and horizontal stretching.
