Question

house sales
number of houses sold
\\(f(x)\\)
\\((2, 8)\\)
\\((6, 6)\\)
\\((12, 4)\\)
\\((0, 0)\\)
\\((10, 2)\\)
number of days

\\(-\frac{4}{3}\\)
\\(-\frac{3}{4}\\)
6
8

Explanation:

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"concepts_used": [
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"new_concepts": [
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"Secant Line Slope"
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"current_concepts": [
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"Average Rate of Change"
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<reasoning>

Identify the interval and coordinates

Using the Graph Interpretation and Function Behavior knowledge points
\[

$$\begin{aligned} &\text{Interval: } [2, 10]\\ &x_1 = 2 \implies f(2) = 8\\ &x_2 = 10 \implies f(10) = 2 \end{aligned}$$

\]

Calculate the average rate of change

Using the Function Behavior knowledge point
\[

$$\begin{aligned} \text{Average Rate of Change} &= \frac{f(10) - f(2)}{10 - 2} \\ &= \frac{2 - 8}{10 - 2} \\ &= \frac{-6}{8} \\ &= -\frac{3}{4} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(-\frac{4}{3}\)</mcq-option>
<mcq-correct>(B) \(-\frac{3}{4}\)</mcq-correct>
<mcq-option>(C) \(6\)</mcq-option>
<mcq-option>(D) \(8\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Average Rate of Change"
]
}
</post_analysis>

Answer:

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"new_concepts": [
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</pre_analysis>

<reasoning>

Identify the interval and coordinates

Using the Graph Interpretation and Function Behavior knowledge points
\[

$$\begin{aligned} &\text{Interval: } [2, 10]\\ &x_1 = 2 \implies f(2) = 8\\ &x_2 = 10 \implies f(10) = 2 \end{aligned}$$

\]

Calculate the average rate of change

Using the Function Behavior knowledge point
\[

$$\begin{aligned} \text{Average Rate of Change} &= \frac{f(10) - f(2)}{10 - 2} \\ &= \frac{2 - 8}{10 - 2} \\ &= \frac{-6}{8} \\ &= -\frac{3}{4} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(-\frac{4}{3}\)</mcq-option>
<mcq-correct>(B) \(-\frac{3}{4}\)</mcq-correct>
<mcq-option>(C) \(6\)</mcq-option>
<mcq-option>(D) \(8\)</mcq-option>
</answer>

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