What is the effect on the $$ x $$-intercept of the graph of $$ f(x)=\sqrt[3]{x} $$ when $$ f(x) $$ is reptaced by $$ f(x+5) $$ ? (1 point) The $$ x $$-intercept shifts up by a distance of 5 . The $$ x $$-intercept shifts down by a distance of 5 . The $$ x $$-intercept shifts to the left by a distance of 5 . The $$ x $$-intercept shifts to the right by a distance of 5 .

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When you replace $$ f(x) $$ with $$ f(x+5) $$, the graph of the function shifts horizontally. Specifically, replacing $$ x $$ with $$ x+5 $$ shifts the graph to the **left** by 5 units.

For the $$ x $$-intercept:
- Original function $$ f(x) = \sqrt[3]{x} $$ has an $$ x $$-intercept at $$ (0, 0) $$.
- The transformed function $$ f(x+5) = \sqrt[3]{x+5} $$ has an $$ x $$-intercept where $$ x+5 = 0 $$, which is $$ x = -5 $$.

Thus, the $$ x $$-intercept shifts to the left by a distance of 5.

**Answer:** The $$ x $$-intercept shifts to the left by a distance of 5 .
The $$ x $$-intercept shifts to the left by a distance of 5.

What is the effect on the -intercept of the graph of when is
reptaced by ? (1 point)
The -intercept shifts up by a distance of 5 .
The -intercept shifts down by a distance of 5 .
The -intercept shifts to the left by a distance of 5 .
The -intercept shifts to the right by a distance of 5 .

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What is the effect on the -intercept of the graph of when is reptaced by ? (1 point) The -intercept shifts up by a distance of 5 . The -intercept shifts down by a distance of 5 . The -intercept shifts to the left by a distance of 5 . The -intercept shifts to the right by a distance of 5 .