identify the horizontal asymptote of each graph.
$f(x) = 6^x$

$\bigcirc$ $y = 0$
$\bigcirc$ $y = 1$
$\bigcirc$ $y = 6$

Question

identify the horizontal asymptote of each graph.
$f(x) = 6^x$

$\bigcirc$ $y = 0$
$\bigcirc$ $y = 1$
$\bigcirc$ $y = 6$

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": [ "Horizontal Asymptotes", "Exponential Function Graphs" ], "new_concepts": [], "current_concepts": [ "Horizontal Asymptotes", "Exponential Function Graphs" ] } ## Analyze the function behavior Using the *Exponential Function Graphs* and *Horizontal Asymptotes* knowledge points $$ \begin{aligned} &\text{For } f(x) = 6^x:\ &\lim_{x \to -\infty} 6^x = 0\ &\text{The curve approaches the line } y = 0 \text{ as } x \to -\infty. \end{aligned} $$ ## Identify the horizontal asymptote Using the *Horizontal Asymptotes* knowledge point $$ \begin{aligned} &\text{The horizontal asymptote is the line } y = 0. \end{aligned} $$

(A) $y = 0$

(B) $y = 1$

(C) $y = 6$

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

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Question

Explanation:

Analyze the function behavior

Identify the horizontal asymptote

Answer: