identify the equation that translates $y = \ln(x)$ five units down.

$y = \ln(x-5)$
$y = \ln(x)+5$
$y = \ln(x+5)$
$y = \ln(x)-5$

Question

identify the equation that translates $y = \ln(x)$ five units down.

$y = \ln(x-5)$
$y = \ln(x)+5$
$y = \ln(x+5)$
$y = \ln(x)-5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Translation", "Vertical Translation", "Logarithmic Transformations" ], "current_concepts": [ "Function Translation", "Vertical Translation", "Logarithmic Transformations" ] } ## Identify the parent function and transformation rule $$ \begin{aligned} &f(x) = \ln(x)\ &g(x) = f(x) - c \quad (c > 0 \text{ translates } f(x) \text{ down by } c \text{ units}) \end{aligned} $$ ## Apply the vertical translation to the function $$ \begin{aligned} &c = 5\ &y = \ln(x) - 5 \end{aligned} $$

(A) $y = \ln(x-5)$

(B) $y = \ln(x)+5$

(C) $y = \ln(x+5)$

(D) $y = \ln(x)-5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Translation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and transformation rule

Apply the vertical translation to the function

Answer: