Question

Which of the following relations is a function?


x
=
7


x
=
|
7
y
|


y
=
7


y
2
=
7
x

Answer 1

Interpret "function" as "y is a function of x" (each x gives at most one y).

- x = 7: vertical line — for x = 7 there are infinitely many y, so not a function.
- x = |7y|: for x > 0 there are two y-values (y = ±x/7), so not a function.
- y = 7: horizontal line — for each x there is exactly one y (y = 7), so this is a function.
- y^2 = 7x: y = ±√(7x) for x ≥ 0, so typically two y-values for a given x, not a function.

Answer: only y = 7 is a function.