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 \#

To reflect the function \( f(x) = \sqrt[3]{x} \) over the \( y \)-axis, we replace \( x \) with \( -x \), yielding \( f(-x) = \sqrt[3]{-x} \). Next, to stretch the graph horizontally by a factor of \( a \), we replace \( x \) with \( \frac{x}{a} \), resulting in \( f\left(-\frac{x}{a}\right) = \sqrt[3]{-\frac{x}{a}} \). Combining these transformations leads us to the function \( f(x) = \sqrt[3]{-\frac{1}{a}x} \). Thus, the best answer is Option \#2: \( f(x)=\sqrt[3]{\frac{1}{-a} x} \).