CONCEPT: The question tests on the area of graphs and functions 

SOLUTION:
 
The equation |x| = 1/y^2 represents the union of the equations:

x = 1/y^2 (Graph is the hyperbola to the right of the Y-axis in the figure)
and
-x = 1/y^2 (Graph is the hyperbola to the left of the Y-axis in the figure)
 Hence (OPTION D)