Question

Which of the following equations represents a function?


x
=
2


y
2
=
x
+
2


y
2
=
x
4
+
2


y
=
x
2

Answer 1

Interpreting “function” as y expressed as a single-valued function of x:

- x = 2: Not a function of x (vertical line gives infinitely many y for x = 2).
- y^2 = x + 2: Not a function (y = ±√(x+2), so many x give two y-values).
- y^2 = x^4 + 2: Not a function (y = ±√(x^4+2), two y-values for every x).
- y = x^2: Yes — for each x there is exactly one y.

So only y = x^2 represents a function.