Question

which of the relations given by the following sets of ordered pairs is a function?
{(5,4),(5,6),(5,8),(5,10),(5,12)}
{(7,3),(-6,8),(-3,5),(0, - 3),(7,11)}
{(-3, - 2),(-2, - 1),(0, - 1),(0,1),(1,2)}
{(5,2),(-4,2),(3,6),(0,4),(-1,2)}

Explanation:

Step1: Recall function definition

A relation is a function if for each input (first - element of the ordered pair), there is exactly one output (second - element of the ordered pair).

Step2: Analyze first set

In the set $\{(5,4),(5,6),(5,8),(5,10),(5,12)\}$, the input $x = 5$ has multiple outputs ($4,6,8,10,12$), so it is not a function.

Step3: Analyze second set

In the set $\{(7,3),(-6,8),(-3,5),(0, - 3),(7,11)\}$, the input $x = 7$ has two outputs ($3$ and $11$), so it is not a function.

Step4: Analyze third set

In the set $\{(-3,-2),(-2,-1),(0,-1),(0,1),(1,2)\}$, the input $x = 0$ has two outputs ($-1$ and $1$), so it is not a function.

Step5: Analyze fourth set

In the set $\{(5,2),(-4,2),(3,6),(0,4),(-1,2)\}$, each input ($5,-4,3,0,-1$) has exactly one output. So it is a function.

Answer:

$\{(5,2),(-4,2),(3,6),(0,4),(-1,2)\}$