Analyze the effect on the $$ y $$-intercept in the graph of $$ f(x)=\sqrt[3]{x} $$ when $$ f(x) $$ is replaced by af $$ (x) $$ and a is positive. (1 point) The $$ y $$-intercept shifts to the left by a distance of $$ a $$. The $$ y $$-intercept does not change. The $$ y $$-intercept shifts up by a distance of $$ a $$. The $$ y $$-intercept shifts down by a distance of $$ a $$.

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When you replace $$ f(x) = \sqrt[3]{x} $$ with $$ af(x) = a\sqrt[3]{x} $$ where $$ a $$ is positive, the transformation affects the vertical scaling of the graph but does not alter the $$ y $$-intercept.

The $$ y $$-intercept occurs where $$ x = 0 $$:
$$
y = a\sqrt[3]{0} = a \cdot 0 = 0
$$
Since the $$ y $$-intercept remains at $$ (0,0) $$, it does not change.

**Answer:** The $$ y $$-intercept does not change.
The $$ y $$-intercept does not change.

Analyze the effect on the -intercept in the graph of when is
replaced by af and a is positive. (1 point)
The -intercept shifts to the left by a distance of .
The -intercept does not change.
The -intercept shifts up by a distance of .
The -intercept shifts down by a distance of .

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Analyze the effect on the -intercept in the graph of when is replaced by af and a is positive. (1 point) The -intercept shifts to the left by a distance of . The -intercept does not change. The -intercept shifts up by a distance of . The -intercept shifts down by a distance of .