determine whether the graph represents a function. if it does represent a function, give its domain and range.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Line Test", "Definition of a Function" ], "new_concepts": [ "Domain and Range of Discrete Relations" ], "current_concepts": [ "Vertical Line Test", "Definition of a Function", "Domain and Range of Discrete Relations" ] } ## Identify the coordinates of the plotted points $$ \{(-2, 1), (3, 3), (3, -2), (5, 2), (5, 3)\} $$ ## Apply the vertical line test $$ \begin{aligned} &x = 3 \implies y = 3 \text{ and } y = -2 \ &x = 5 \implies y = 2 \text{ and } y = 3 \end{aligned} $$ ## Determine if the relation is a function $$ \text{Since vertical lines } x = 3 \text{ and } x = 5 \text{ intersect more than one point, it is not a function.} $$ The graph does not represent a function because it fails the vertical line test (the inputs $x = 3$ and $x = 5$ are each mapped to multiple $y$-values). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Definition of a Function" ] }

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Explanation:

Identify the coordinates of the plotted points

Apply the vertical line test

Determine if the relation is a function

Answer: