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.

When you replace \( f(x) \) with \( 7 f(x) \), you are stretching the graph vertically by a factor of 7. This means that for each x-value on the graph of \( f(x) = \sqrt[3]{x} \), the corresponding y-value is multiplied by 7. So, while the graph does not shift left or right, it does get taller! Instead of moving up or down, it stretches up, amplifying the output values. To visualize this, imagine taking the original shape of the cubic-root graph and pulling it upwards without changing its overall form. A small hill becomes a towering mountain, but the "footprint" on the x-axis remains the same. If you started with a graph touching the x-axis at (0,0), after the transformation, it stretches straight up, reaching the same x values but leaving a much bolder imprint in terms of output!