the parent function (f(x) = x^3) is translated to form (g(x)), as shown on the graph. the translated function can be written in the form (g(x) = (x - h)^3 + k).

what are the values of (h) and (k)?

* (h = 4), (k = -2)
* (h = -4), (k = -2)
* (h = 4), (k = 2)
* (h = -4), (k = 2)

Question

the parent function (f(x) = x^3) is translated to form (g(x)), as shown on the graph. the translated function can be written in the form (g(x) = (x - h)^3 + k).

what are the values of (h) and (k)?

* (h = 4), (k = -2)
* (h = -4), (k = -2)
* (h = 4), (k = 2)
* (h = -4), (k = 2)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Cubic Function Transformations" ], "new_concepts": [], "current_concepts": [ "Cubic Function Transformations", "Function Transformations" ] } ## Identify the inflection point of the parent function $$ (0, 0) $$ ## Identify the inflection point of the translated function $$ (4, -2) $$ ## Determine the translation parameters $$ \begin{aligned} g(x) &= (x - h)^3 + k \ h &= 4 \ k &= -2 \end{aligned} $$

h = 4 k = -2

h = -4 k = -2

h = 4 k = 2

h = -4 k = 2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Cubic Function Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the inflection point of the parent function

Identify the inflection point of the translated function

Determine the translation parameters

Answer: