What is the effect on the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( -2 f(x) \) ? (1 point) The graph is reflected across the \( x \)-axis and has been stretched horizontally. The graph is reflected across the \( x \)-axis and has been stretched vertically. The graph is reflected across the \( y \)-axis and has been compressed vertically. The graph is reflected across the \( y \)-axis and has been compressed horizontally.

When you replace \( f(x) = \sqrt[3]{x} \) with \( -2f(x) \), the transformation involves two main changes: 1. **Reflection across the \( x \)-axis:** The negative sign (\(-\)) flips the graph vertically. 2. **Vertical Stretch:** The factor of 2 (\( \times 2 \)) stretches the graph away from the \( x \)-axis by a factor of 2. Thus, the graph of \( f(x) = \sqrt[3]{x} \) is both reflected across the \( x \)-axis and stretched vertically when replaced by \( -2f(x) \). **Answer:** The graph is reflected across the \( x \)-axis and has been stretched vertically.