Answer: the first option, {(1, 2), (4, –2), (8, 3), (9, –3)}
Explanation:
1) A function is a rule (relation) that permits relate an input unambiguously to an output.
In {(1, 2), (4, –2), (8, 3), (9, –3)}, clearly this the relation:
pari input output
(1, 2) 1 2
(4, –2) 4 -2
(8, 3) 8 3
(9, –3) 9 -3
2) y² = 16 − x² is not a function, because you cannot pair unambiguously some y values with some x values.
For example: the value x = 2 is related with both y = √12 and - √12, which you can prove:
x = 2 ⇒ y² = 16 - (2)² = 16 - 4 = 12 ⇒ y = +/- √12
3) You can prove 2x² + y² = 5 is not a function is the same way:
2x² + y² = 5 ⇒ y² = 5 - 2x², so for most x-values in the domain there are two different possible values of y.
3) x = 7
The input can only be 7 and the output can be any number, so does not relate 7 with any particular number: it can be -2000, 0, √5, .... any number.
