What is the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( -5 f(x) \) ? (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 does not change. The \( y \)-intercept shifts up by a distance of 5 .

When we replace \( f(x) \) with \( -5 f(x) \), we effectively multiply the output of the function by -5. The original function \( f(x) = \sqrt[3]{x} \) has a \( y \)-intercept at point (0, 0). After the transformation, the new function becomes \( g(x) = -5\sqrt[3]{x} \). For \( x = 0 \), \( g(0) = -5\sqrt[3]{0} = -5 \times 0 = 0 \). So, the \( y \)-intercept at (0, 0) remains unchanged even though the output of all y-values (except at the intercept) is scaled and inverted. The answer is: The \( y \)-intercept does not change.