consider the table representing a rational function.

which equation could represent a vertical asymptote of the graph of the function?

$x = 0$
$y = 0$
$x = -1$
$y = -1$

Question

consider the table representing a rational function.

which equation could represent a vertical asymptote of the graph of the function?

$x = 0$
$y = 0$
$x = -1$
$y = -1$

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 behavior near undefined point Using the *Vertical Asymptotes* and *Rational Functions* knowledge points $$ \begin{aligned} &\lim_{x \to -1^{-}} f(x) = -\infty \quad (\text{values drop from } -10 \text{ to } -111.\overline{1})\ &\lim_{x \to -1^{+}} f(x) = +\infty \quad (\text{values rise from } 10 \text{ to } 100)\ &f(-1) \text{ is undefined} \end{aligned} $$ ## Determine vertical asymptote equation Using the *Vertical Asymptotes* knowledge point $$ x = -1 $$

(A) $x = 0$

(B) $y = 0$

(C) $x = -1$

(D) $y = -1$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify behavior near undefined point

Determine vertical asymptote equation

Answer: