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)

Explanation:

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<reasoning>

Identify the inflection point of the parent function

\[
(0, 0)
\]

Identify the inflection point of the translated function

\[
(4, -2)
\]

Determine the translation parameters

\[

$$\begin{aligned} g(x) &= (x - h)^3 + k \\ h &= 4 \\ k &= -2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>h = 4
k = -2</mcq-correct>
<mcq-option>h = -4
k = -2</mcq-option>
<mcq-option>h = 4
k = 2</mcq-option>
<mcq-option>h = -4
k = 2</mcq-option>
</answer>

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"Mathematics",
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Answer:

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</pre_analysis>

<reasoning>

Identify the inflection point of the parent function

\[
(0, 0)
\]

Identify the inflection point of the translated function

\[
(4, -2)
\]

Determine the translation parameters

\[

$$\begin{aligned} g(x) &= (x - h)^3 + k \\ h &= 4 \\ k &= -2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>h = 4
k = -2</mcq-correct>
<mcq-option>h = -4
k = -2</mcq-option>
<mcq-option>h = 4
k = 2</mcq-option>
<mcq-option>h = -4
k = 2</mcq-option>
</answer>

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