which statement best describes (g(x) = \sqrt3{x + 6} - 8) and the parent function (f(x) = \sqrt3{x})?

the domains of (g(x)) and (f(x)) are the same, but their ranges are not the same.
the ranges of (g(x)) and (f(x)) are the same, but their domains are not the same.
the ranges of (g(x)) and (f(x)) are the same, and their domains are also the same.
the domains of (g(x)) and (f(x)) are the not the same, and their ranges are also not the same.

Question

which statement best describes (g(x) = \sqrt3{x + 6} - 8) and the parent function (f(x) = \sqrt3{x})?

the domains of (g(x)) and (f(x)) are the same, but their ranges are not the same.
the ranges of (g(x)) and (f(x)) are the same, but their domains are not the same.
the ranges of (g(x)) and (f(x)) are the same, and their domains are also the same.
the domains of (g(x)) and (f(x)) are the not the same, and their ranges are also not the same.

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 Domain", "Odd Roots" ], "new_concepts": [], "current_concepts": [ "Cube Root Domain", "Odd Roots", "Range of Radical Functions" ] } ## Determine the domain of both functions $$ \begin{aligned} &\text{Domain of } f(x) = \sqrt[3]{x} \text{ is } (-\infty, \infty)\ &\text{Domain of } g(x) = \sqrt[3]{x+6}-8 \text{ is } (-\infty, \infty) \end{aligned} $$ ## Determine the range of both functions $$ \begin{aligned} &\text{Range of } f(x) = \sqrt[3]{x} \text{ is } (-\infty, \infty)\ &\text{Range of } g(x) = \sqrt[3]{x+6}-8 \text{ is } (-\infty, \infty) \end{aligned} $$ ## Compare domains and ranges $$ \begin{aligned} &\text{Domains: } \text{Same } ((-\infty, \infty))\ &\text{Ranges: } \text{Same } ((-\infty, \infty)) \end{aligned} $$

The domains of $g(x)$ and $f(x)$ are the same, but their ranges are not the same.

The ranges of $g(x)$ and $f(x)$ are the same, but their domains are not the same.

The ranges of $g(x)$ and $f(x)$ are the same, and their domains are also the same.

The domains of $g(x)$ and $f(x)$ are the not the same, and their ranges are also not the same.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Cube Root Domain" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the domain of both functions

Determine the range of both functions

Compare domains and ranges

Answer: