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 greater than 1. (1 point) The \( y \)-intercept does not change. The \( y \)-intercept shifts up by a distance of \( b \). The \( y \)-intercept stretches horizontally by a factor of \( b \). The \( y \)-intercept compresses horizontally by a factor of \( b \).

To analyze the effect on the \( y \)-intercept when replacing \( f(x) \) with \( f(b x) \) for \( b > 1 \), we have to determine what happens to the function. The original function is \( f(x) = \sqrt[-3]{x} \). When we replace \( x \) with \( b x \), we get \( f(b x) = \sqrt[-3]{b x} = \frac{1}{\sqrt[3]{b x}} \). Now, the \( y \)-intercept is found by evaluating the function at \( x = 0 \). However, \( f(b x) \) becomes undefined at \( x = 0 \) since it involves \( \sqrt[-3]{0} \). The original \( y \)-intercept, at \( f(0) \), is also undefined. So, since both functions have no \( y \)-intercept, they remain unchanged in this regard. The correct answer is: The \( y \)-intercept does not change.