If \( f(x)=x^{3} \), what is the effect on its graph when \( f(x) \) is replaced by \( f(-2 x) \) ? (1 point) a horizontal stretch and reflection over the \( y \)-axis a horizontal compression and reflection over the \( y \)-axis a vertical stretch and reflection over the \( x \)-axis a vertical compression and reflection over the \( x \)-axis

When \( f(x) \) is replaced by \( f(-2x) \), the transformation involves two main changes: 1. **Reflection over the \( y \)-axis**: The negative sign inside the function argument \( (-2x) \) causes a reflection across the \( y \)-axis. 2. **Horizontal Compression**: The factor of 2 inside the function argument compresses the graph horizontally by a factor of \( \frac{1}{2} \). Therefore, the graph undergoes a **horizontal compression** and a **reflection over the \( y \)-axis**. **Answer:** a horizontal compression and reflection over the \( y \)-axis