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.

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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 ($$ 	imes 2 $$) 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.
The graph is reflected across the $$ x $$-axis and stretched vertically.

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