which expression can be used to determine the average rate of change in $f(x)$ over the interval $2, 9$?

- $f(9 - 2)$
- $f(9) - f(2)$
- $\frac{f(9 - 2)}{9 - 2}$
- $\frac{f(9) - f(2)}{9 - 2}$

Question

which expression can be used to determine the average rate of change in $f(x)$ over the interval $2, 9$?

- $f(9 - 2)$
- $f(9) - f(2)$
- $\frac{f(9 - 2)}{9 - 2}$
- $\frac{f(9) - f(2)}{9 - 2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Graphical Analysis" ] } ## State the average rate of change formula $$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$ ## Substitute the given interval values $$ \begin{aligned} &[a, b] = [2, 9]\ &\text{Average Rate of Change} = \frac{f(9) - f(2)}{9 - 2} \end{aligned} $$

(A) $f(9 - 2)$

(B) $f(9) - f(2)$

(C) $\frac{f(9 - 2)}{9 - 2}$

(D) $\frac{f(9) - f(2)}{9 - 2}$

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

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Question

Explanation:

State the average rate of change formula

Substitute the given interval values

Answer: