Çözüldü Function Graph - Limit

From the University of Oxford:

https://i72.servimg.com/u/f72/19/97/10/39/oxford22.png
https://www.maths.ox.ac.uk/system/files/attachments/test2023b.pdf (The last question)
Solution: https://www.maths.ox.ac.uk/system/files/attachments/websolutions23b.pdf

Note:
The right side is x^2 - x^4 - 6·y^2·x^2 and moving the two terms with negative signs to the left side yields the equation;
(x + y)^4 = x^2
x + y = ∓√x
y = -x ∓ √x
x > √x....(I)
lim (x → ∞) y = lim (x → ∞) (-x ∓ √x)....(II)
Because of the inequality at (I), the limit at (II) is -∞, so the only graph that satisfies the condition x → ∞ ⇒ y → -∞ is (d).