Question

5/22
which of the following is a function?

x | f(x)
2 | -2
0 | 0
2 | 2
8 | 4

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

Explanation:

Step1: Recall function definition

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

Step2: Check top-left graph

Apply vertical line test: Any vertical line drawn on the graph intersects the line at most once. This means each x has one y-value.

Step3: Check top-right table

The input $x=2$ has two outputs: $-2$ and $2$. This violates the function definition.

Step4: Check bottom-left set

The input $x=6$ has two outputs: $1$ and $-3$. This violates the function definition.

Step5: Check bottom-right mapping

The input $5$ maps to two outputs: $4$ and $-4$. This violates the function definition.

Answer:

The top-left graph (the linear graph passing through the grid) is a function.