Why does x^4 not have an inflection point algebraicly

This is basically asking if each transformation is an isometry, which maps a triangle to a congruent triangle.

(x,y)⇒(-y,x)  That's an isometry, not scaling x or y.  I think it's a 90 degree rotation.  CONGRUENT

(x,y)⇒(x-2,y-1/2)  No scaling, pure translation. CONGRUENT

(x,y)⇒(2x,2y)  That's a double scaling so NOT CONGRUENT

(x,y)⇒(-x,y)  That's a reflection.  CONGRUENT

(x,y)⇒(1/2 x, 1/2 y) Scaling again, NOT CONGRUENT