Question

which of the following are functions?
$j = \\{(-1,-1), (-2,1), (-4,2), (1,-2), (2,-2), (6,-2)\\}$
$q = \\{(4,-2), (8,2), (0,7), (-2,3), (6,9), (5,5)\\}$
$x = \\{(-1,0), (3,2), (6,4), (8,9), (13,12), (15,16)\\}$
$v = \\{(0,-1), (2,1), (2,5), (6,9), (8,-6), (15,16)\\}$
$l = \\{(-1,-2), (0,0), (1,3), (4,6), (8,9), (15,11)\\}$
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Explanation:

Step1: Recall function definition

A relation is a function if every input (first element of each ordered pair) has exactly one output (second element). No repeated inputs allowed.

Step2: Check set J

Inputs: $-1, -2, -4, 1, 2, 6$ (all unique).

Step3: Check set Q

Inputs: $4, 8, 0, -2, 6, 5$ (all unique).

Step4: Check set X

Inputs: $-1, 3, 6, 8, 13, 15$ (all unique).

Step5: Check set V

Inputs: $0, 2, 2, 6, 8, 15$ (input $2$ repeats, paired with $1$ and $5$).

Step6: Check set L

Inputs: $-1, 0, 1, 4, 8, 15$ (all unique).

Answer:

J = {(-1,-1), (-2,1), (-4,2), (1,-2), (2,-2), (6,-2)}
Q = {(4,-2), (8,2), (0,7), (-2,3), (6,9), (5,5)}
X = {(-1,0), (3,2), (6,4), (8,9), (13,12), (15,16)}
L = {(-1,-2), (0,0), (1,3), (4,6), (8,9), (15,11)}