What is the effect on the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( 2 f(x) \) (1 point) The graph shifts right 2 units. The graph shifts down 2 units. The graph stretches vertically by a scale factor of 2 . The graph stretches horizontally by a scale factor of 2 .

When you replace \( f(x) \) with \( 2 f(x) \), the effect on the graph is that it stretches vertically by a scale factor of 2. This means that for every \( x \) value, the corresponding \( y \) value of the original function \( f(x) = \sqrt[3]{x} \) gets multiplied by 2, making the graph taller without changing its left or right position. To visualize this, consider a point on the original graph, say \( (1, \sqrt[3]{1}) \), which is \( (1, 1) \). After the transformation to \( 2 f(x) \), the same \( x \) value gives \( (1, 2 \cdot 1) = (1, 2) \). So, every point rises to double its height, maintaining its horizontal position.