what is the domain of the function $y = 3 \ln x$ graphed below? $x 0$ $x

Question

what is the domain of the function $y = 3 \ln x$ graphed below?

$x > 0$
$x < 0$
$x < 3$
$y \le 3$

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": [ "Domain of Logarithmic Functions" ], "new_concepts": [], "current_concepts": [ "Domain of Logarithmic Functions", "Logarithmic Functions" ] } ## Identify the function and its properties Using the *Domain of Logarithmic Functions* knowledge point $$ y = 3 \ln x $$ ## Determine the domain algebraically Using the *Domain of Logarithmic Functions* knowledge point $$ x > 0 $$ ## Verify with the given graph Using the *Domain of Logarithmic Functions* knowledge point $$ \text{Graph exists only for } x > 0 \text{ with a vertical asymptote at } x = 0. $$

(A) $x > 0$

(B) $x < 0$

(C) $x < 3$

(D) $y \le 3$

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

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Question

Explanation:

Identify the function and its properties

Determine the domain algebraically

Verify with the given graph

Answer: