Analyze the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( f(b x) \) and \( b \) is less than -1. (1 point) The \( y \)-intercept shifts up by a distance of \( b \). The \( y \)-intercept stretches horizontally. The \( y \)-intercept does not change. The \( y \)-intercept compresses horizontally.

When we replace \( f(x) \) with \( f(bx) \) for \( b < -1 \), we are effectively analyzing the new function \( f(bx) = \sqrt[3]{bx} \). Since the \( y \)-intercept is determined by the function value at \( x = 0 \), we calculate \( f(b \cdot 0) = f(0) = \sqrt[3]{0} \), which still equals 0. Thus, the \( y \)-intercept does not change; it's still at the point (0,0) regardless of the value of \( b \). So, the correct answer is: The \( y \)-intercept does not change.