Question

which of the relations given by the following sets of ordered pairs is not a function? {(-4, -2), (-1, -1), (-1, 1), (3, 5), (7, 10)} {(-6, 4), (-3, -2), (0, 5), (1, -2), (2, 3)} {(-8, 3), (-6, 5), (-4, 2), (-2, 7), (-1, 4)} {(5, 0), (4, 0), (3, 0), (2, 0), (1, 0)}

Explanation:

Step1: Recall function definition

A relation is a function if every input (x-value) has exactly one output (y-value).

Step2: Check Option 1

Examine x-values: $-4, -1, -1, 3, 7$. The x-value $-1$ appears twice, paired with $-1$ and $1$.

Step3: Check Option 2

Examine x-values: $-6, -3, 0, 1, 2$. All x-values are unique.

Step4: Check Option 3

Examine x-values: $-8, -6, -4, -2, -1$. All x-values are unique.

Step5: Check Option 4

Examine x-values: $5, 4, 3, 2, 1$. All x-values are unique.

Answer:

$\{ (-4, -2), (-1, -1), (-1, 1), (3, 5), (7, 10)\}$