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": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Lines" ], "new_concepts": [ "Vertical Line Test" ], "current_concepts": [ "Vertical Lines", "Vertical Line Test" ] } ## Apply the vertical line test $$ \text{A graph represents a function if and only if no vertical line intersects the graph more than once.} $$ ## Analyze the piecewise boundary $$ \begin{aligned} &\text{At the jump discontinuity, the upper piece ends with a solid dot (included point).} \ &\text{The lower piece starts with a solid dot (included point) at the same } x\text{-coordinate.} \ &\text{A vertical line drawn through this } x\text{-coordinate intersects the graph at two distinct points.} \end{aligned} $$ ## Determine function status $$ \text{Since a vertical line intersects the graph at two points, the graph is not a function.} $$

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 piecewise boundary

Determine function status

Answer: