Question

determine whether the following graph represents a function.
the graph does 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 the graph at most once. For this graph, a vertical line (e.g., $x=0$) intersects the graph at two points: $(0, 3)$ and $(0, -3)$.

Step2: Interpret the Test Result

Since at least one vertical line intersects the graph more than once, the graph fails the vertical line test. This means one input ($x$-value) maps to multiple outputs ($y$-values).

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 two outputs: $y = 3$ and $y = -3$.