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

When you replace \( f(x) \) with \( f(2x) \), the effect on the graph is a horizontal compression. This occurs because multiplying the input \( x \) by 2 means that the output values change more rapidly, effectively squishing the graph towards the y-axis. So, each point on the graph now appears at half the distance from the y-axis compared to the original function. To visualize this, think about the original curve of \( \sqrt[3]{x} \). When substituting \( f(2x) \), for any given output, the input is halved, bringing the points closer together. Thus, the function displays a more narrow shape, making it a horizontal compression by a factor of 2.