Question

determine whether the following graph represents a function.
answer attempt 1 out of 2
the graph does not represent a function because at least one input is mapped to a single output. for example, the input ( x = ) is only mapped to the approximate output of ( y = ).

Explanation:

Step1: Apply Vertical Line Test

A graph represents a function if any vertical line drawn intersects it at most once. For this diamond-shaped graph, vertical lines (e.g., $x=0$) intersect at 2 points.

Step2: Correct the reasoning

The graph fails the test because one input maps to multiple outputs, not a single one.

Step3: Pick an example input

Choose $x=0$, which maps to two $y$-values: $y=6$ and $y=0$.

Answer:

The graph does not represent a function because at least one input is mapped to more than one output. For example, the input $x = 0$ is mapped to the approximate outputs of $y = 6$ and $y = 0$.