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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change", "Graphical Analysis" ], "new_concepts": [ "Average Rate of Change on Interval" ], "current_concepts": [ "Average Rate of Change", "Graphical Analysis" ] } ## Identify coordinates from the graph $$ \begin{aligned} &\text{At } x = 0,\quad f(0) = 0\ &\text{At } x = 3,\quad f(3) = 8\ &\text{At } x = 10,\quad f(10) = 5\ &\text{At } x = 12,\quad f(12) = 9 \end{aligned} $$ ## Calculate average rate of change on interval [0, 13] $$ \begin{aligned} &\text{Line segment from } (10, 5) \text{ to } (12, 9) \text{ has slope: } m = \frac{9 - 5}{12 - 10} = 2\ &\text{Equation for } x \ge 10: y - 5 = 2(x - 10) \implies y = 2x - 15\ &\text{At } x = 13:\quad f(13) = 2(13) - 15 = 11\ &\text{Average rate of change on } [0, 13]: \frac{f(13) - f(0)}{13 - 0} = \frac{11 - 0}{13} = \frac{11}{13} \end{aligned} $$

(A) $\frac{1}{3}$

(B) $\frac{4}{13}$

(C) $\frac{11}{13}$

(D) $\frac{11}{8}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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Explanation:

Identify coordinates from the graph

Calculate average rate of change on interval [0, 13]

Answer: