Question

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Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). We use the vertical line test: if any vertical line intersects the graph more than once, it is not a function.

Step2: Analyze each graph

• Top - Left Graph: Draw a vertical line (mentally or physically). There are parts where a vertical line would intersect the graph more than once (the "S" - shaped curve has overlapping x - values with different y - values). So, it is not a function.
• Top - Right Graph: The graph has a vertical asymptote (dashed line), but for all x - values (except near the asymptote), each x has one y. Using the vertical line test, any vertical line will intersect the graph at most once. So, it could be a function.
• Bottom - Left Graph: This is a hyperbola - like graph, and it fails the vertical line test (a vertical line will intersect both branches, meaning one x has two y - values). So, it is not a function.
• Bottom - Right Graph: This is a "V" - shaped graph but with a "point" in the middle that creates a situation where a vertical line (at the vertex's x - value) would intersect the graph more than once? Wait, no, actually, looking at the graph, it is a non - function because there is a point where a vertical line would cross two segments. Wait, no, re - examining: the bottom - right graph has a "corner" but actually, when we apply the vertical line test, there is an x - value (at the vertex) where a vertical line would intersect the graph twice. So, it is not a function.

Wait, maybe the question is to identify which graphs are not functions. But if we assume the question is to find which graph is a function, the top - right graph passes the vertical line test. If the question is to find which are not functions, the top - left, bottom - left, and bottom - right are not functions (since they fail the vertical line test), and the top - right is a function.

Assuming the question is to identify the graph that represents a function (using vertical line test):

Step3: Confirm with vertical line test

The vertical line test states that a graph represents a function if and only if no vertical line intersects the graph at more than one point. The top - right graph (the one with the vertical dashed asymptote) satisfies this, while the others do not.

Answer:

The Top - Right Graph (the graph in the top - right cell of the grid)