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

To reflect the function \( f(x) = \sqrt[3]{x} \) over the \( y \)-axis, we replace \( x \) with \( -x \), resulting in \( f(-x) = \sqrt[3]{-x} \). For a horizontal stretch by a factor of 4, we replace \( x \) with \( \frac{x}{4} \), leading to the new function \( f\left(-\frac{x}{4}\right) = \sqrt[3]{-\frac{x}{4}} \). Thus, the correct transformation gives us the new function: \( f(x) = \sqrt[3]{-\frac{1}{4} x} \), which matches Option #3. Option #3: \( f(x)=\sqrt[3]{-\frac{1}{4} x} \)