What is the effect on the \( y \)-intercept in the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( f(-5 x) \) ? (1 point) The \( y \)-intercept is reflected over the \( x \)-axis and shifts up by a distance of 5 . The \( y \)-intercept is reflected over the \( x \)-axis and compresses horizontally by a factor of 5 . The \( y \)-intercept is reflected over the \( x \)-axis and stretches horizontally. The \( y \)-intercept does not change.

To find the \( y \)-intercept of the function \( f(x) = \sqrt[3]{x} \), we evaluate it at \( x = 0 \), resulting in \( f(0) = \sqrt[3]{0} = 0 \). Now consider the transformed function \( f(-5x) = \sqrt[3]{-5x} \). The \( y \)-intercept occurs when \( x = 0 \) as well, giving \( f(-5 \cdot 0) = \sqrt[3]{0} = 0 \) again. Therefore, the \( y \)-intercept does not change, remaining at the origin. Now, let's have some fun imagining how this reflection and transformation might appear in a graphical world! Picture a giant graph climbing a mountain range, where every point is a unique and quirky creature. As \( f(x) \) takes its original shape, when we replace it with \( f(-5x) \), imagine the creature doing an acrobatics move! It flips, but since both forms still land at the same point on the \( y \)-axis, it ends up at the same place with a big smile. Same spot, just some twisty fun along the way!