match each section of the function to the description of how the $y$-value changes as the $x$-value increases.

a $\
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b $\
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c $\
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d $\
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increases quickly increases slowly decreases slowly decreases quickly

Question

match each section of the function to the description of how the $y$-value changes as the $x$-value increases.

a $\
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b $\
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c $\
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d $\
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increases quickly increases slowly decreases slowly decreases quickly

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope of a Line", "Linear Graphs" ], "new_concepts": [ "Qualitative Graphs", "Rate of Change Analysis" ], "current_concepts": [ "Slope of a Line", "Linear Graphs", "Qualitative Graphs", "Rate of Change Analysis" ] } ## Analyze the slopes of each segment $$ \begin{aligned} &\text{Segment A: positive slope, gentle incline} \implies \text{increases slowly} \ &\text{Segment B: negative slope, steep decline} \implies \text{decreases quickly} \ &\text{Segment C: positive slope, steep incline} \implies \text{increases quickly} \ &\text{Segment D: negative slope, gentle decline} \implies \text{decreases slowly} \end{aligned} $$ ## Match segments to descriptions $$ \begin{aligned} &\text{A} \longrightarrow \text{increases slowly} \ &\text{B} \longrightarrow \text{decreases quickly} \ &\text{C} \longrightarrow \text{increases quickly} \ &\text{D} \longrightarrow \text{decreases slowly} \end{aligned} $$ Match each section of the function to the description of how the $y$-value changes as the $x$-value increases: * **A** $\longrightarrow$ **increases slowly** * **B** $\longrightarrow$ **decreases quickly** * **C** $\longrightarrow$ **increases quickly** * **D** $\longrightarrow$ **decreases slowly** { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Qualitative Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the slopes of each segment

Match segments to descriptions

Answer: