Question

vWhich of the following relations is a function?


x
=
7


x
=
|
7
y
|


y
=
7


y
2
=
7
x

Answer 1

Only y = 7.

Reason: A relation is a function (y as a function of x) if each x-value gives exactly one y-value.
- x = 7: the single x-value 7 pairs with infinitely many y's → not a function.
- x = |7y|: for x > 0 there are two y-values (±x/7) → not a function.
- y = 7: every x gives exactly one y (7) → a function (constant function).
- y^2 = 7x: for x > 0 there are two y-values (±√(7x)) → not a function.