Given the function \( f(x)=\sqrt[3]{x} \), what is the new function when it is reflected over the \( y \)-axis and horizontally compressed? Option \#1: \( f(x)=\sqrt[3]{-3 x} \) Option \#2: \( f(x)=\sqrt[3]{3 x} \) Option \#3: \( f(x)=\sqrt[3]{\frac{1}{3} x} \) Option \#4: \( f(x)=\sqrt[3]{-\frac{1}{3} x} \) (1 point) The best answer is Option \#

To reflect the function \( f(x) = \sqrt[3]{x} \) over the \( y \)-axis, you replace \( x \) with \( -x \), resulting in \( f(-x) = \sqrt[3]{-x} \). To horizontally compress this function, you multiply \( x \) by a factor greater than 1, which is often \( k \) for compression. If we choose \( k = 3 \), the function transforms to \( f(-3x) = \sqrt[3]{-3x} \). Therefore, the transformed function is \( f(x) = \sqrt[3]{-3x} \). So the best answer is Option #1: \( f(x) = \sqrt[3]{-3 x} \).