Analyze the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by af \( (x) \) and a is positive. (1 point) The \( y \)-intercept shifts to the left by a distance of \( a \). The \( y \)-intercept does not change. The \( y \)-intercept shifts up by a distance of \( a \). The \( y \)-intercept shifts down by a distance of \( a \).

When you replace \( f(x) \) with \( af(x) \), where \( a \) is a positive constant, the entire graph of the function is scaled vertically by a factor of \( a \). This means that the \( y \)-values of all points on the graph increase, including the \( y \)-intercept. The original \( y \)-intercept of \( f(x) = \sqrt[3]{x} \) occurs at the point (0, 0). When you substitute \( f(x) \) with \( af(x) \), the new \( y \)-intercept becomes \( (0, a \cdot \sqrt[3]{0}) = (0, 0) \). Thus, the \( y \)-intercept remains unchanged, leading to the conclusion that the answer is: the \( y \)-intercept does not change.