Question

given that \\(y = (-5)^x\\), find the missing output values for the following table.

\\(\

$$\begin{array}{|c|c|}\\hline x \\text{ input} & y \\text{ output} \\\\\\hline 1 & \\\\\\hline 2 & \\\\\\hline 3 & \\\\\\hline 4 & \\\\\\hline 5 & \\\\\\hline\\end{array}$$

\\)

enter your answers in the order they would appear in the table, top to bottom, separated by commas.

Explanation:

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"new_concepts": [
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<reasoning>

Evaluate the function for each input value

\[

$$\begin{aligned} x = 1: \quad &y = (-5)^1 = -5 \\ x = 2: \quad &y = (-5)^2 = 25 \\ x = 3: \quad &y = (-5)^3 = -125 \\ x = 4: \quad &y = (-5)^4 = 625 \\ x = 5: \quad &y = (-5)^5 = -3125 \end{aligned}$$

\]

List the outputs in order

\[
-5, 25, -125, 625, -3125
\]
</reasoning>

<answer>
Given that \(y = (-5)^x\), find the missing output values for the following table.

Enter your answers in the order they would appear in the table, top to bottom, separated by commas: <blank>-5, 25, -125, 625, -3125</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponential Function Evaluation"
]
}
</post_analysis>

Answer:

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"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
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"Geometric Sequence",
"Explicit Formula"
],
"new_concepts": [
"Exponential Function Evaluation"
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"Exponential Function Evaluation"
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<reasoning>

Evaluate the function for each input value

\[

$$\begin{aligned} x = 1: \quad &y = (-5)^1 = -5 \\ x = 2: \quad &y = (-5)^2 = 25 \\ x = 3: \quad &y = (-5)^3 = -125 \\ x = 4: \quad &y = (-5)^4 = 625 \\ x = 5: \quad &y = (-5)^5 = -3125 \end{aligned}$$

\]

List the outputs in order

\[
-5, 25, -125, 625, -3125
\]
</reasoning>

<answer>
Given that \(y = (-5)^x\), find the missing output values for the following table.

Enter your answers in the order they would appear in the table, top to bottom, separated by commas: <blank>-5, 25, -125, 625, -3125</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponential Function Evaluation"
]
}
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