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

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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
The graph undergoes a horizontal compression and a reflection over the $$ y $$-axis.

If , what is the effect on its graph when is replaced by ?
(1 point)
a horizontal stretch and reflection over the -axis
a horizontal compression and reflection over the -axis
a vertical stretch and reflection over the -axis
a vertical compression and reflection over the -axis

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If , what is the effect on its graph when is replaced by ? (1 point) a horizontal stretch and reflection over the -axis a horizontal compression and reflection over the -axis a vertical stretch and reflection over the -axis a vertical compression and reflection over the -axis