Question

the graph of (f(x) = 6(0.25)^x) and its reflection across the y-axis, (g(x)), are shown.

what is the domain of (g(x))?

all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0

Explanation:

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<reasoning>

Identify the function and transformation

\[
f(x) = 6(0.25)^x
\]
\[
g(x) = f(-x) = 6(0.25)^{-x}
\]

Determine the domain of the transformed function

\[
\text{Domain of } f(x): x \in \mathbb{R}
\]
\[
\text{Domain of } g(x): -x \in \mathbb{R} \implies x \in \mathbb{R}
\]

Match with the given options

\[
\text{Domain} = \text{all real numbers}
\]
</reasoning>

<answer>
<mcq-correct>all real numbers</mcq-correct>
<mcq-option>all real numbers less than 0</mcq-option>
<mcq-option>all real numbers greater than 0</mcq-option>
<mcq-option>all real numbers greater than or equal to 0</mcq-option>
</answer>

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{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Domain and Range"
]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the function and transformation

\[
f(x) = 6(0.25)^x
\]
\[
g(x) = f(-x) = 6(0.25)^{-x}
\]

Determine the domain of the transformed function

\[
\text{Domain of } f(x): x \in \mathbb{R}
\]
\[
\text{Domain of } g(x): -x \in \mathbb{R} \implies x \in \mathbb{R}
\]

Match with the given options

\[
\text{Domain} = \text{all real numbers}
\]
</reasoning>

<answer>
<mcq-correct>all real numbers</mcq-correct>
<mcq-option>all real numbers less than 0</mcq-option>
<mcq-option>all real numbers greater than 0</mcq-option>
<mcq-option>all real numbers greater than or equal to 0</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
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"Algebra",
"Domain and Range"
]
}
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