determine whether the graph is that of a function. an open dot indicates that the point does not belong on the graph.

is the graph the graph of a function?
no
yes

Question

determine whether the graph is that of a function. an open dot indicates that the point does not belong on the graph.

is the graph the graph of a function?
no
yes

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Line Test" ], "new_concepts": [], "current_concepts": [ "Vertical Line Test", "Function Behavior" ] } ## Apply the vertical line test $$ \text{For any vertical line } x = c, \text{ the line intersects the graph at most once.} $$ ## Analyze the endpoints of the piecewise segments $$ \begin{aligned} &\text{At the boundary value where the segments split:} \ &\text{The left segment ends with a solid dot (point is included).} \ &\text{The right segment starts with a solid dot (point is included).} \ &\text{A vertical line passing through this } x\text{-value intersects two solid dots simultaneously.} \end{aligned} $$ ## Determine function status $$ \text{Since a vertical line intersects the graph at more than one point, it is not a function.} $$

No

Yes

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertical Line Test" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the vertical line test

Analyze the endpoints of the piecewise segments

Determine function status

Answer: