what is the range of the function $ y = \sqrt3{x+8} $?

$ -\infty

Question

what is the range of the function $ y = \sqrt3{x+8} $?

$ -\infty < y < \infty $
$ -8 < y < \infty $
$ 0 \le y < \infty $
$ 2 \le y < \infty $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Cube Root Function" ], "new_concepts": [ "Range of Cube Root Functions" ], "current_concepts": [ "Cube Root Function", "Range of Cube Root Functions" ] } ## Analyze the parent function Using the *Cube Root Function* knowledge point $$ \begin{aligned} &f(x) = \sqrt[3]{x}\ &\text{Domain: } -\infty < x < \infty\ &\text{Range: } -\infty < y < \infty \end{aligned} $$ ## Apply horizontal translation Using the *Cube Root Function* knowledge point $$ \begin{aligned} &y = \sqrt[3]{x+8}\ &\text{Shift: } 8\text{ units left}\ &\text{Domain: } -\infty < x < \infty\ &\text{Range: } -\infty < y < \infty \end{aligned} $$

(A) $-\infty < y < \infty$

(B) $-8 < y < \infty$

(C) $0 \le y < \infty$

(D) $2 \le y < \infty$

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QUESTION IMAGE

Question

Explanation:

Analyze the parent function

Apply horizontal translation

Answer: