select the lines that represent functions.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Definition" ], "new_concepts": [], "current_concepts": [ "Function Definition", "Relations and Functions" ] } ## Apply the vertical line test to each graph $$ \begin{aligned} &\text{Vertical line at } x = -6 \text{ intersects the vertical segment infinitely many times (Not a function).} \ &\text{Any vertical line intersects the horizontal segment at } y = 4 \text{ at most once (Function).} \ &\text{Vertical line at } x = -4 \text{ intersects the S-shaped curve three times (Not a function).} \ &\text{Any vertical line intersects the diagonal line segment from } (1,1) \text{ to } (4,4) \text{ at most once (Function).} \ &\text{Any vertical line intersects the parabola-like curve at most once (Function).} \end{aligned} $$ ## Identify the lines representing functions $$ \begin{aligned} &\text{Horizontal segment at } y = 4 \ &\text{Diagonal segment from } (1,1) \text{ to } (4,4) \ &\text{Parabolic curve in the fourth quadrant} \end{aligned} $$ The lines that represent functions are: 1. The horizontal line segment at $y = 4$ (spanning from $x = -4$ to $x = -1$). 2. The diagonal line segment from $(1, 1)$ to $(4, 4)$. 3. The U-shaped curve (parabola) in the lower-right quadrant (spanning from $x = 2$ to $x = 5$). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Function Definition" ] }

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Apply the vertical line test to each graph

Identify the lines representing functions

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