which of the functions is reflected across the $x$-axis and shifted to left from the parent function $y = \sqrt{x}$?

$y = -2\sqrt{x + 3}$
$y = 2\sqrt{x + 3}$

Question

which of the functions is reflected across the $x$-axis and shifted to left from the parent function $y = \sqrt{x}$?

$y = -2\sqrt{x + 3}$
$y = 2\sqrt{x + 3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Root Function", "Function Transformations", "Square Root Transformations" ], "new_concepts": [], "current_concepts": [ "Square Root Function", "Function Transformations", "Square Root Transformations" ] } ## Analyze reflection across the x-axis $$ y = -\sqrt{x} $$ ## Analyze horizontal shift to the left $$ y = -\sqrt{x + c},\quad c > 0 $$ ## Match with the given options $$ y = -2\sqrt{x + 3} $$

(A) $y = -2\sqrt{x + 3}$

(B) $y = 2\sqrt{x + 3}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze reflection across the x-axis

Analyze horizontal shift to the left

Match with the given options

Answer: