Given the function $$ f(x)=\sqrt[3]{x} $$, what is the new function when it is reflected over the $$ y $$-axis, stretching horizontally? Assume that a is a positive integer greater than 1 . Option \#1: $$ f(x)=\sqrt[3]{-a x} $$ Option \#2: $$ f(x)=\sqrt[3]{\frac{1}{-a} x} $$ Option \#3: $$ f(x)=\sqrt[3]{a x} $$ Option \#4: $$ f(x)=\sqrt[3]{\frac{1}{a} x} $$ (1 point) The best answer is Option \#

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The correct transformation involves both reflecting over the $$ y $$-axis and stretching horizontally by a factor of $$ a $$.

1. **Reflection over the $$ y $$-axis:** Replace $$ x $$ with $$ -x $$, resulting in $$ f(-x) = \sqrt[3]{-x} $$.
2. **Horizontal Stretch by $$ a $$:** Replace $$ x $$ with $$ \frac{x}{a} $$, resulting in $$ f\left(\frac{x}{a}\right) = \sqrt[3]{\frac{x}{a}} $$.

Combining these transformations, the new function is:
$$
f\left(-\frac{x}{a}\right) = \sqrt[3]{-\frac{x}{a}} = \sqrt[3]{\frac{-x}{a}}
$$

This corresponds to **Option #2**.

**Answer:** Option #2
The new function after reflecting over the $$ y $$-axis and stretching horizontally by a factor of $$ a $$ is $$ f(x) = \sqrt[3]{\frac{1}{-a} x} $$. So, the correct option is **Option #2**.

Given the function , what is the new function when it is reflected over the
-axis, stretching horizontally? Assume that a is a positive integer greater than 1 .
Option #1:
Option #2:
Option #3:
Option #4:
(1 point)
The best answer is Option #

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Given the function , what is the new function when it is reflected over the -axis, stretching horizontally? Assume that a is a positive integer greater than 1 . Option #1: Option #2: Option #3: Option #4: (1 point) The best answer is Option #