Question

1. which set of ordered pairs represents y as a function of x?

{(4, √17), (2, √6), (1, √3), (1, √10)}
{(-7, 2.9), (-15, 5.9), (-15, 8.9), (-7, 11.9)}
{(11.1, 7), (5.1, 4), (12.1, 5), (6.1, 7)}
{(√1, -3), (√2, -4), (√1, -5), (√6, -7)}

Explanation:

Step1: Recall function definition

A relation is a function if for each input $x$ there is exactly one output $y$.

Step2: Check first set

In $\{(4,\sqrt{17}),(2,\sqrt{6}),(1,\sqrt{3}),(1,\sqrt{10})\}$, $x = 1$ has two different $y$-values ($\sqrt{3}$ and $\sqrt{10}$), so it's not a function.

Step3: Check second set

In $\{(-7,2.9),(-15,5.9),(-15,8.9),(-7,11.9)\}$, $x=-7$ has two $y$-values and $x = - 15$ has two $y$-values, so it's not a function.

Step4: Check third set

In $\{(11.1,7),(5.1,4),(12.1,5),(6.1,7)\}$, each $x$-value has exactly one $y$-value, so it is a function.

Step5: Check fourth set

In $\{(\sqrt{1}, - 3),(\sqrt{2},-4),(\sqrt{1},-5),(\sqrt{6},-7)\}$, since $\sqrt{1}=1$ and $x = 1$ has two $y$-values ($-3$ and $-5$), so it's not a function.

Answer:

$\{(11.1,7),(5.1,4),(12.1,5),(6.1,7)\}$