...Mechanic Sixth
The sixth degree components, top pair, are the outer independent roots of a hexic function.
In this flat view of the complex plane, one readily sees the hyperbolesque shape of the independent roots.

To me it recalls Excalibur, or another sword of lore not for the ordinary hand; (note the white hilt).

In this metaphor, hilt and blade are the function itself: (x to the sixth plus four-thirds x).

It's not easy to tell from this view, but it passes behind the curtain;

(note the sharp color-change below the guard, and the much subtler one above it).

The guard would be its dependent roots, again parabola-like in form. .They too are behind the curtain.

The inner independent roots, (those closer to the hilt), pass to the inside.
This faded view, (with fog and perspective effects),

details one of the inner independent roots, (grub-like at left), as it passes inside the curtain.

A look at its mate, (at right) reveals that these curves are not purely hyperbolesque, for it bends twice.

And, now that the Y axis is out of silhouette, the shape of the "real function" begins to appear.

Lastly, it clarifies that in the figures above, purple is closer to the viewer than gold.
In this profile view, the shape of the hexic is revealed, its being a shark-nose facing down.

It should be noted that a hexic function is capable of considerably more activity than this,

but as it's got only one complicating degree, (four-thirds x), its behavior is rather sedate.

In any case, the whisker on the nose is, (are), what I've been calling the "dependent roots".

And then moving rightward, the parallel pairs are the "inner" and "outer" "independent roots".
Finally, a portrait view. .The hexic itself is the vertical line at center,

its dependent roots the parabolesque shape which opens beneath it.

The "inner" root curves -- remember this is only my usage -- are, in this case, at far left and right.

The "outer" "independent root curves" are, then, at center left and center right.