Analyze the effect on the $$ y $$-intercept in the graph of $$ f(x)=\sqrt[-3]{x} $$ when $$ f(x) $$ is replaced by $$ f(b x) $$ and $$ b $$ is greater than 1. (1 point) The $$ y $$-intercept does not change. The $$ y $$-intercept shifts up by a distance of $$ b $$. The $$ y $$-intercept stretches horizontally by a factor of $$ b $$. The $$ y $$-intercept compresses horizontally by a factor of $$ b $$.

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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 $$ f(x) = \sqrt[-3]{x} = x^{-1/3} $$:

$$
f(0) = 0^{-1/3} \text{ is undefined.}
$$

However, considering the transformation $$ f(bx) $$:

$$
f(bx) = (bx)^{-1/3} = \frac{1}{\sqrt[3]{bx}}
$$

When $$ x = 0 $$:

$$
f(b \cdot 0) = f(0) = \frac{1}{\sqrt[3]{0}} \text{ remains undefined.}
$$

This indicates that the $$ y $$-intercept does not exist for either the original or the transformed function. Since the $$ y $$-intercept remains unchanged (both are undefined), the correct option is:

**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 and is greater than 1. (1 point)
The -intercept does not change.
The -intercept shifts up by a distance of .
The -intercept stretches horizontally by a factor of .
The -intercept compresses horizontally by a factor of .

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Analyze the effect on the -intercept in the graph of when is replaced by and is greater than 1. (1 point) The -intercept does not change. The -intercept shifts up by a distance of . The -intercept stretches horizontally by a factor of . The -intercept compresses horizontally by a factor of .