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:

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.

Answer:

• A) \(-9, 0, 3\)
• B) \(-9, 0, 9\)
• C) \(-3, 0, 9\)
• D) \(-3, 0, 3\) (Correct answer)