How does the graph of \( f(x)=\sqrt[3]{x} \) change when \( f(x) \) is replaced by \( f(7 x) \) ? (1 point) The graph moves down 7 units. The graph moves to the right 7 units. The graph moves up 7 units. The graph does not shift left or right.

When you replace \( f(x) \) with \( f(7x) \), you're compressing the graph horizontally by a factor of 7. This means that for every value of \( x \), the corresponding output \( f(x) \) is achieved at \( 7x \) instead, effectively pulling the graph closer to the y-axis. So, it doesn’t move left or right at all; rather, it becomes more concentrated around the y-axis. To visualize it, think of it like squishing a sponge – the overall shape stays the same, but it gets narrower. So the correct answer here is that "The graph does not shift left or right."