# Question Video: Determining If a Graphed Relation Is a Function Mathematics

Which of the following relations represents a function given that 𝑥 is the input and 𝑦 is the output?

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### Video Transcript

Which of the following relations represents a function given that 𝑥 is the input and 𝑦 is the output?

To answer this question, we will use the vertical line test. This is a graphical way of working out whether a graph represents a function. If a graph represents a function, any vertical line will intersect the function at most once. We will therefore add a vertical line to our diagrams and inspect the number of points of intersection with the curves. In figure (A), we observe that if we add the vertical line 𝑥 equals five, the line intersects the curve twice. This means that graph (A) cannot represent a function. The vertical line 𝑥 equals negative four intersects the curve of graph (B) exactly once. We can translate this vertical line by any distance horizontally, and this will always be the case. We can therefore conclude that graph (B) represents a function. The correct answer is (B).

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