which function has no horizontal asymptote?

$ f(x) = \frac{2x - 1}{3x^2} $

$ f(x) = \frac{x - 1}{3x} $

$ f(x) = \frac{2x^2}{3x - 1} $

$ f(x) = \frac{3x^2}{x^2 - 1} $

Question

which function has no horizontal asymptote?

$ f(x) = \frac{2x - 1}{3x^2} $

$ f(x) = \frac{x - 1}{3x} $

$ f(x) = \frac{2x^2}{3x - 1} $

$ f(x) = \frac{3x^2}{x^2 - 1} $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Horizontal Asymptotes" ], "new_concepts": [], "current_concepts": [ "Horizontal Asymptotes", "Rational Functions" ] } ## Compare degrees of numerator and denominator $$ \begin{aligned} &\text{For } f(x) = \frac{2x-1}{3x^2}: \text{degree of numerator } (1) < \text{degree of denominator } (2) \implies y = 0\ &\text{For } f(x) = \frac{x-1}{3x}: \text{degree of numerator } (1) = \text{degree of denominator } (1) \implies y = \frac{1}{3}\ &\text{For } f(x) = \frac{2x^2}{3x-1}: \text{degree of numerator } (2) > \text{degree of denominator } (1) \implies \text{No horizontal asymptote}\ &\text{For } f(x) = \frac{3x^2}{x^2-1}: \text{degree of numerator } (2) = \text{degree of denominator } (2) \implies y = 3 \end{aligned} $$

(A) $f(x) = \frac{2x-1}{3x^2}$

(B) $f(x) = \frac{x-1}{3x}$

(C) $f(x) = \frac{2x^2}{3x-1}$

(D) $f(x) = \frac{3x^2}{x^2-1}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Horizontal Asymptotes" ] }

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QUESTION IMAGE

Question

Explanation:

Compare degrees of numerator and denominator

Answer: