What is the effect on the \( x \)-intercept of the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is reptaced by \( f(x+5) \) ? (1 point) The \( x \)-intercept shifts up by a distance of 5 . The \( x \)-intercept shifts down by a distance of 5 . The \( x \)-intercept shifts to the left by a distance of 5 . The \( x \)-intercept shifts to the right by a distance of 5 .

When we replace \( f(x) \) with \( f(x+5) \), it effectively translates the graph of the function to the left by 5 units. For the graph of \( f(x) = \sqrt[3]{x} \), the original \( x \)-intercept is at the point (0,0). With the transformation to \( f(x+5) = \sqrt[3]{x+5} \), the \( x \)-intercept moves to the point (-5,0). So, the correct answer is: The \( x \)-intercept shifts to the left by a distance of 5.