which function represents g(x), a reflection of $f(x) = \frac{1}{2}(3)^x$ across the y-axis?

$g(x) = 2(3)^x$
$g(x) = -\frac{1}{2}(3)^x$
$g(x) = \frac{1}{2}(3)^{-x}$
$g(x) = 2(3)^{-x}$

Question

which function represents g(x), a reflection of $f(x) = \frac{1}{2}(3)^x$ across the y-axis?

$g(x) = 2(3)^x$
$g(x) = -\frac{1}{2}(3)^x$
$g(x) = \frac{1}{2}(3)^{-x}$
$g(x) = 2(3)^{-x}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions", "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Function Transformations", "Reflections" ] } ## Identify the rule for reflection across the y-axis $$ g(x) = f(-x) $$ ## Substitute the given function into the transformation rule $$ \begin{aligned} f(x) &= \frac{1}{2}(3)^x \ g(x) &= f(-x) = \frac{1}{2}(3)^{-x} \end{aligned} $$

(A) $g(x) = 2(3)^x$

(B) $g(x) = -\frac{1}{2}(3)^x$

(C) $g(x) = \frac{1}{2}(3)^{-x}$

(D) $g(x) = 2(3)^{-x}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the rule for reflection across the y-axis

Substitute the given function into the transformation rule

Answer: