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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vertical Asymptotes", "Horizontal Asymptotes" ], "new_concepts": [], "current_concepts": [ "Vertical Asymptotes", "Horizontal Asymptotes", "Rational Functions" ] } ## Find the vertical asymptote condition Using the *Vertical Asymptotes* knowledge point $$ \begin{aligned} &x + a = 0 \implies x = -a\ &-a = 1 \implies a = -1 \end{aligned} $$ ## Find the horizontal asymptote condition Using the *Horizontal Asymptotes* knowledge point $$ \begin{aligned} &\lim_{x \to \infty} \frac{2x^m}{x + a} = 2\ &m = 1 \implies \lim_{x \to \infty} \frac{2x}{x - 1} = 2 \end{aligned} $$ ## Match the parameters to the options Using the *Rational Functions* knowledge point $$ \begin{aligned} &a = -1\ &m = 1 \end{aligned} $$

(A) $a = -1, m = 0$

(B) $a = 1, m = 0$

(C) $a = -1, m = 1$

(D) $a = 1, m = 1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Asymptotes of Rational Functions" ] }

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Explanation:

Find the vertical asymptote condition

Find the horizontal asymptote condition

Match the parameters to the options

Answer: