describe how the graph of the parent function $y = \sqrt3{x}$ is transformed when graphing $y = \sqrt3{8x} - 3$.

the graph is translated 3 units dropdown

Question

describe how the graph of the parent function $y = \sqrt3{x}$ is transformed when graphing $y = \sqrt3{8x} - 3$.

the graph is translated 3 units dropdown

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": [ "Cube Root Transformations", "Vertical Translation" ], "new_concepts": [], "current_concepts": [ "Cube Root Transformations", "Vertical Translation", "Horizontal Translation", "Vertical Dilation" ] } ## Simplify the transformed function Using the *Cube Root Transformations* knowledge point $$ \begin{aligned} y &= \sqrt[3]{8x} - 3 \ &= \sqrt[3]{8} \cdot \sqrt[3]{x} - 3 \ &= 2\sqrt[3]{x} - 3 \end{aligned} $$ ## Identify the vertical translation Using the *Vertical Translation* knowledge point $$ \begin{aligned} &f(x) = 2\sqrt[3]{x} \ &g(x) = f(x) - 3 \end{aligned} $$ Subtracting 3 from the function shifts the graph 3 units down. Describe how the graph of the parent function $y = \sqrt[3]{x}$ is transformed when graphing $y = \sqrt[3]{8x} - 3$. The graph is translated 3 units down. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Cube Root Transformations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the transformed function

Identify the vertical translation

Answer: