what is the smallest x-value in this function?

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

$(?, \quad)$

Question

what is the smallest x-value in this function?

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

$(?, \quad)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Domain of Radical Functions", "Radicand Inequality" ], "new_concepts": [], "current_concepts": [ "Domain of Radical Functions", "Radicand Inequality", "Radical Function Vertex" ] } ## 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 $$ \begin{aligned} y &= \sqrt{5 - 5} - 3 \ y &= -3 \end{aligned} $$ What is the smallest x-value in this function? (5, -3) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Domain of Radical Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the radicand inequality

Solve for the minimum x-value

Determine the corresponding y-value

Answer: