Question

question 17 (5 points)

what values complete the table if \\(y = \sqrt3{x}\\)?

a) \\(-9, 0, 3\\)
b) \\(9, 0, 9\\)
c) \\(-3, 0, 9\\)
d) \\(-3, 0, 3\\)

Explanation:

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<reasoning>

Identify the given function and inputs

We are given the function:
\[y = \sqrt[3]{x}\]
We need to evaluate this function for the input values of \(x\) given in the table:
\[x = -27, \quad x = 0, \quad x = 27\]

Evaluate the function at x = -27

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{-27} = -3
\]

Evaluate the function at x = 0

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{0} = 0
\]

Evaluate the function at x = 27

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{27} = 3
\]

Combine the results

The calculated \(y\)-values corresponding to \(x = -27, 0, 27\) are:
\[-3, 0, 3\]
This sequence matches option D.
</reasoning>

<answer>
<mcq-option>A) \(-9, 0, 3\)</mcq-option>
<mcq-option>B) \(-9, 0, 9\)</mcq-option>
<mcq-option>C) \(-3, 0, 9\)</mcq-option>
<mcq-correct>D) \(-3, 0, 3\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify the given function and inputs

We are given the function:
\[y = \sqrt[3]{x}\]
We need to evaluate this function for the input values of \(x\) given in the table:
\[x = -27, \quad x = 0, \quad x = 27\]

Evaluate the function at x = -27

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{-27} = -3
\]

Evaluate the function at x = 0

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{0} = 0
\]

Evaluate the function at x = 27

Using the Algebraic Expression Evaluation knowledge point
\[
y = \sqrt[3]{27} = 3
\]

Combine the results

The calculated \(y\)-values corresponding to \(x = -27, 0, 27\) are:
\[-3, 0, 3\]
This sequence matches option D.
</reasoning>

<answer>
<mcq-option>A) \(-9, 0, 3\)</mcq-option>
<mcq-option>B) \(-9, 0, 9\)</mcq-option>
<mcq-option>C) \(-3, 0, 9\)</mcq-option>
<mcq-correct>D) \(-3, 0, 3\)</mcq-correct>
</answer>

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