What is the effect on the $$ y $$-intercept in the graph of $$ f(x)=\sqrt[3]{x} $$ when $$ f(x) $$ is replaced by $$ -5 f(x) $$ ? (1 point) The $$ y $$-intercept shifts to the right by a distance of 5 . The $$ y $$-intercept shifts down by a distance of 5 . The $$ y $$-intercept does not change. The $$ y $$-intercept shifts up by a distance of 5 .

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UpStudy AI · Accepted Answer

The $$ y $$-intercept of a function is determined by the value of the function when $$ x = 0 $$.

For the original function $$ f(x) = \sqrt[3]{x} $$:
$$
f(0) = \sqrt[3]{0} = 0
$$

When replacing $$ f(x) $$ with $$ -5f(x) $$:
$$
-5f(0) = -5 \times 0 = 0
$$

Since the $$ y $$-intercept remains $$ 0 $$ after the transformation, it does not change.

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

What is the effect on the -intercept in the graph of when is
replaced by ? (1 point)
The -intercept shifts to the right by a distance of 5 .
The -intercept shifts down by a distance of 5 .
The -intercept does not change.
The -intercept shifts up by a distance of 5 .

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What is the effect on the -intercept in the graph of when is replaced by ? (1 point) The -intercept shifts to the right by a distance of 5 . The -intercept shifts down by a distance of 5 . The -intercept does not change. The -intercept shifts up by a distance of 5 .