Which of the following expressions represents a function? {(1, 2), (4, –2), (8, 3), (9, –3)} y2 = 16 − x2 2x2 + y2 = 5 x = 7

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.