Question

question 3 of 5
select the correct answer.
which of the following sets of ordered pairs represents a function?
{ (10,5), (10,-5), (5,10), (5,-10) }
{ (3,5), (-17,-5), (3,-5), (-17,5) }
{ (-6,-1), (13,8), (1,6), (1,-10) }
{ (10,5), (-10,-5), (5,10), (-5,-10) }

Explanation:

Step1: Recall function definition

A set of ordered pairs is a function if each input (first element of the pair) has exactly one output (second element of the pair).

Step2: Check Option 1

Inputs: $10, 10, 5, 5$. The input $10$ maps to $5$ and $-5$; input $5$ maps to $10$ and $-10$. This is not a function.

Step3: Check Option 2

Inputs: $3, -17, 3, -17$. The input $3$ maps to $5$ and $-5$; input $-17$ maps to $-5$ and $5$. This is not a function.

Step4: Check Option 3

Inputs: $-6, 13, 1, 1$. The input $1$ maps to $6$ and $-10$. This is not a function.

Step5: Check Option 4

Inputs: $10, -10, 5, -5$. Each input has exactly one unique output: $10\to5$, $-10\to-5$, $5\to10$, $-5\to-10$. This is a function.

Answer:

$\{(10,5), (-10,-5), (5,10), (-5,-10)\}$