the graph of $g(x)$ is the result of translating the graph of $f(x) = 3^x$ six units to the right. what is the equation of $g(x)$?

$g(x) = 3^{x - 6}$
$g(x) = 3^{x + 6}$
$g(x) = 3^x - 6$
$g(x) = 3^x + 6$

Question

the graph of $g(x)$ is the result of translating the graph of $f(x) = 3^x$ six units to the right. what is the equation of $g(x)$?

$g(x) = 3^{x - 6}$
$g(x) = 3^{x + 6}$
$g(x) = 3^x - 6$
$g(x) = 3^x + 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Exponential Functions" ] } ## Identify the horizontal translation rule $$ y = f(x - h) \implies \text{translation of } f(x) \text{ by } h \text{ units to the right} $$ ## Apply translation to the given function $$ \begin{aligned} f(x) &= 3^x \ h &= 6 \ g(x) &= f(x - 6) = 3^{x - 6} \end{aligned} $$

(A) $g(x) = 3^{x - 6}$

(B) $g(x) = 3^{x + 6}$

(C) $g(x) = 3^x - 6$

(D) $g(x) = 3^x + 6$

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

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QUESTION IMAGE

Question

Explanation:

Identify the horizontal translation rule

Apply translation to the given function

Answer: