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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Functions", "Asymptotes", "Domain and Range" ], "new_concepts": [], "current_concepts": [ "Rational Functions", "Asymptotes", "Domain and Range" ] } ## Identify asymptotes from the graph $$ \begin{aligned} &\text{Vertical asymptote: } x = 1 \ &\text{Horizontal asymptote: } y = -1 \end{aligned} $$ ## Determine domain and range $$ \begin{aligned} &\text{Domain: } (-\infty, 1) \cup (1, \infty) \ &\text{Range: } (-\infty, -1) \cup (-1, \infty) \end{aligned} $$ ## Identify intercepts from the graph $$ \begin{aligned} &\text{x-intercept(s): } \text{None} \ &\text{y-intercept(s): } -2 \quad (\text{or coordinate } (0, -2)) \end{aligned} $$ ## Question 1 (a) Write the equations for all vertical and horizontal asymptotes: - Vertical asymptote(s): $x = 1$ - Horizontal asymptote(s): $y = -1$ ## Question 2 (b) Find the domain and range of $f$: - Domain: $(-\infty, 1) \cup (1, \infty)$ - Range: $(-\infty, -1) \cup (-1, \infty)$ ## Question 3 (c) Find all $x$-intercepts and $y$-intercepts: - $x$-intercept(s): None - $y$-intercept(s): $-2$ { "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 from the graph

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