How does the graph of $$ f(x)=\sqrt[3]{x} $$ change when $$ f(x) $$ is replaced by $$ 7 f(x) $$ ? The graph does not shift left or right. The graph moves down 7 units. The graph moves up 7 units. The graph moves to the right 7 units.

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To determine how the graph of $$ f(x) = \sqrt[3]{x} $$ changes when $$ f(x) $$ is replaced by $$ 7f(x) $$, we need to understand the effect of multiplying the function by a constant.

When a function $$ f(x) $$ is multiplied by a constant $$ c $$, the graph of the function is stretched vertically by a factor of $$ c $$. This means that the graph of $$ 7f(x) $$ will be the same as the graph of $$ f(x) $$ but stretched vertically by a factor of 7.

Therefore, the graph of $$ f(x) = \sqrt[3]{x} $$ when replaced by $$ 7f(x) $$ will move up 7 units vertically.

So, the correct answer is: The graph moves up 7 units.
The graph moves up 7 units.

How does the graph of change when is replaced by ?
The graph does not shift left or right.
The graph moves down 7 units.
The graph moves up 7 units.
The graph moves to the right 7 units.

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How does the graph of change when is replaced by ? The graph does not shift left or right. The graph moves down 7 units. The graph moves up 7 units. The graph moves to the right 7 units.