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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Rational Functions", "Asymptotes", "Domain and Range" ], "current_concepts": [ "Rational Functions", "Asymptotes", "Domain and Range", "Intercepts" ] } ## Identify asymptotes from the graph $$ \begin{aligned} &\text{Vertical asymptotes: } x = -1, \quad x = 2\ &\text{Horizontal asymptote: } y = 1 \end{aligned} $$ ## Determine domain and range $$ \begin{aligned} &\text{Domain: } (-\infty, -1) \cup (-1, 2) \cup (2, \infty)\ &\text{Range: } (-\infty, 1) \cup (1, \infty) \end{aligned} $$ ## Identify intercepts $$ \begin{aligned} &\text{x-intercepts: None}\ &\text{y-intercept: None} \end{aligned} $$ ## Question (a) * **Vertical asymptote(s):** $x = -1, 2$ * **Horizontal asymptote(s):** $y = 1$ ## Question (b) * **Domain:** $(-\infty, -1) \cup (-1, 2) \cup (2, \infty)$ * **Range:** $(-\infty, 1)$ ## Question (c) * **x-intercept(s):** None * **y-intercept(s):** None { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Rational Functions" ] }

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Identify asymptotes from the graph

Determine domain and range

Identify intercepts

Answer:

Question (a)

Question (b)

Question (c)