what are the vertical asymptotes of
$f(x) = \frac{10}{x^2 - 1}$

$x = -1$
$x = 0$
$x = 1$
$x = 10$

Question

what are the vertical asymptotes of
$f(x) = \frac{10}{x^2 - 1}$

$x = -1$
  $x = 0$
  $x = 1$
  $x = 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vertical Asymptotes", "Rational Functions" ], "new_concepts": [], "current_concepts": [ "Vertical Asymptotes", "Rational Functions" ] } ## Identify the function and conditions for vertical asymptotes Using the *Vertical Asymptotes* and *Rational Functions* knowledge points $$ \begin{aligned} &f(x) = \frac{10}{x^2 - 1}\ &x^2 - 1 = 0 \implies (x - 1)(x + 1) = 0\ &x = 1 \quad \text{or} \quad x = -1 \end{aligned} $$ ## Verify the options Using the *Vertical Asymptotes* knowledge point $$ \begin{aligned} &\text{The vertical asymptotes are } x = -1 \text{ and } x = 1. \end{aligned} $$

(A) $x = -1$

(B) $x = 0$

(C) $x = 1$

(D) $x = 10$

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

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Question

Explanation:

Identify the function and conditions for vertical asymptotes

Verify the options

Answer: