the domain of $y = \sqrt{x-5} - 1$ is
$x \ge 5$

the range of $y = \sqrt{x-5} - 1$ is

Question

the domain of $y = \sqrt{x-5} - 1$ is
$x \ge 5$

the range of $y = \sqrt{x-5} - 1$ is

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": [ "Square Root Function Domain", "Square Root Function Range" ], "new_concepts": [], "current_concepts": [ "Square Root Function Domain", "Square Root Function Range", "Square Root Function Transformations" ] } ## Determine the domain of the function Using the *Square Root Function Domain* knowledge point $$ \begin{aligned} x - 5 &\ge 0 \ x &\ge 5 \end{aligned} $$ ## Determine the range of the function Using the *Square Root Function Range* knowledge point $$ \begin{aligned} \sqrt{x - 5} &\ge 0 \ \sqrt{x - 5} - 1 &\ge -1 \ y &\ge -1 \end{aligned} $$ The domain of $y = \sqrt{x-5}-1$ is $x \ge 5$ The range of $y = \sqrt{x-5}-1$ is $y \ge -1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Function Range" ] }

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Explanation:

Determine the domain of the function

Determine the range of the function

Answer: