Given the function $$ f(x)=x^{3} $$, analyze the changes in the graph to determine which statement best describes the graph of $$ g(x)=-\frac{1}{2} f(x) $$. (1 point) The graph will undergo a vertical stretch because $$ 0

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Given the function $$ f(x)=x^{3} $$, analyze the changes in the graph to determine which statement best describes the graph of $$ g(x)=-\frac{1}{2} f(x) $$. (1 point) The graph will undergo a vertical stretch because $$ 0<|a|<1 $$. The graph will undergo a reflection due to the negative sign, and a vertical compression because $$ 0<|a|<1 $$. The graph will undergo a reflection due to the negative sign, and a vertical stretch because $$ |a|>1 $$. The graph will only undergo a reflection due to the negative sign.

UpStudy AI · Accepted Answer

The correct statement is:

**The graph will undergo a reflection due to the negative sign, and a vertical compression because $$ 0 < |a| < 1 $$.**

**Explanation:**
- The negative sign in $$ g(x) = -\frac{1}{2}f(x) $$ causes a reflection over the x-axis.
- The coefficient $$ \frac{1}{2} $$ (where $$ 0 < |\frac{1}{2}| < 1 $$) results in a vertical compression of the graph by a factor of $$ \frac{1}{2} $$.

**Answer:**
The graph will undergo a reflection due to the negative sign, and a vertical compression because $$ 0<|a|<1 $$.
The graph will undergo a reflection over the x-axis and a vertical compression by a factor of $$ \frac{1}{2} $$.

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