Question

which relation below is a function? press to hear a reminder or hint for this problem. ordered pairs are written in the form ((x, y)), where (x) is the input value and (y) is the output value. examine each relation to see if any input value, (x), is paired with multiple output values, (y). a ({(-6, 8), (-4, 5), (-2, 2), (0, -1), (-2, -4)}) b ({(1, 2), (2, 3), (3, 2), (2, 1), (1, 0)}) c ({(-6, 8), (-4, 5), (-2, 2), (0, -1), (-2, 2)}) d ({(-6, 8), (-4, 5), (-2, 2), (0, -1), (-4, 2)})

Explanation:

Step1: Recall function definition

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

Step2: Check Option A

Input $x=-2$ pairs with $y=2$ and $y=-4$. Not a function.

Step3: Check Option B

Input $x=1$ pairs with $y=2$ and $y=0$; $x=2$ pairs with $y=3$ and $y=1$. Not a function.

Step4: Check Option C

Each $x$-value has only one $y$-value: $x=-6\to8$, $x=-4\to5$, $x=-2\to2$, $x=0\to-1$. This is a function.

Step5: Check Option D

Input $x=-4$ pairs with $y=5$ and $y=2$. Not a function.

Answer:

C. $\{(-6, 8), (-4, 5), (-2, 2), (0, -1), (-2, 2)\}$