Question

what is the smallest x-value in this function?

\\y = \sqrt{x - 5} - 3\\

\\((?, \quad)\\)

Explanation:

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<reasoning>

Set up the radicand inequality

Using the Radicand Inequality and Domain of Radical Functions knowledge points
\[
x - 5 \ge 0
\]

Solve for the minimum x-value

Using the Domain of Radical Functions knowledge point
\[
x \ge 5
\]

Determine the corresponding y-value

Using the Domain of Radical Functions knowledge point
\[

$$\begin{aligned} y &= \sqrt{5 - 5} - 3 \\ y &= -3 \end{aligned}$$

\]
</reasoning>

<answer>
What is the smallest x-value in this function?
(<blank>5</blank>, <blank>-3</blank>)
</answer>

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"Mathematics",
"Algebra",
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]
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Answer:

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</pre_analysis>

<reasoning>

Set up the radicand inequality

Using the Radicand Inequality and Domain of Radical Functions knowledge points
\[
x - 5 \ge 0
\]

Solve for the minimum x-value

Using the Domain of Radical Functions knowledge point
\[
x \ge 5
\]

Determine the corresponding y-value

Using the Domain of Radical Functions knowledge point
\[

$$\begin{aligned} y &= \sqrt{5 - 5} - 3 \\ y &= -3 \end{aligned}$$

\]
</reasoning>

<answer>
What is the smallest x-value in this function?
(<blank>5</blank>, <blank>-3</blank>)
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Domain of Radical Functions"
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