the graph shows a vertical translation of (y = \sqrt3{x}).

what is the range of the translated function?

$\{y | y

Question

the graph shows a vertical translation of (y = \sqrt3{x}).

what is the range of the translated function?

$\{y | y < 0\}$
$\{y | y \ge 0\}$
$\{y | y \text{ is a natural number}\}$
$\{y | y \text{ is a real number}\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Cube Root Transformations", "Odd Roots" ], "new_concepts": [], "current_concepts": [ "Cube Root Transformations", "Odd Roots", "Range of Radical Functions" ] } ## Identify the parent function and its range $$ \begin{aligned} &f(x) = \sqrt[3]{x} \ &\text{Range}(f) = \{y \mid y \in \mathbb{R}\} \end{aligned} $$ ## Determine the effect of a vertical translation $$ \begin{aligned} &g(x) = \sqrt[3]{x} + k \ &\text{Range}(g) = \{y + k \mid y \in \mathbb{R}\} = \{y \mid y \in \mathbb{R}\} \end{aligned} $$ ## Match with the given options $$ \text{Range} = \{y \mid y \text{ is a real number}\} $$

{y|y < 0}

{y|y $\ge$ 0}

{y|y is a natural number}

{y|y is a real number}

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Range of Radical Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and its range

Determine the effect of a vertical translation

Match with the given options

Answer: