the graph of $f(x)$ is given on the right.
which roots of $f(x)$ have an odd multiplicity?
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Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Root Multiplicity", "Polynomial Graph Behavior" ], "new_concepts": [], "current_concepts": [ "Root Multiplicity", "Polynomial Graph Behavior" ] } ## Identify the x-intercepts (roots) from the graph $$ x = -1, \quad x = 1, \quad x = 3 $$ ## Determine the behavior of the graph at each root $$ \begin{aligned} &\text{At } x = -1: \text{The graph crosses the x-axis (odd multiplicity).} \ &\text{At } x = 1: \text{The graph touches and turns around at the x-axis (even multiplicity).} \ &\text{At } x = 3: \text{The graph crosses the x-axis (odd multiplicity).} \end{aligned} $$ ## Select the roots with odd multiplicity $$ x = -1, \quad x = 3 $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Root Multiplicity" ] }

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Question

Explanation:

Identify the x-intercepts (roots) from the graph

Determine the behavior of the graph at each root

Select the roots with odd multiplicity

Answer: