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

When we replace \( f(x) \) with \( f(x) + 5 \), we are essentially shifting the entire graph of the function vertically. The original function \( f(x) = \sqrt[3]{x} \) intersects the \( y \)-axis at the point \( (0,0) \). After adding 5, the new function \( f(x) + 5 = \sqrt[3]{x} + 5 \) will intersect the \( y \)-axis at the point \( (0, 5) \). This means the \( y \)-intercept shifts up by a distance of 5. So, the correct answer is: The \( y \)-intercept shifts up by a distance of 5.