The graph of the cube root function is given by \( y = \sqrt[3]{x} \). To find the point where it intersects the y-axis, we set \( x = 0 \).
Substituting \( x = 0 \) into the function:
\[ y = \sqrt[3]{0} = 0 \]
Thus, the graph intersects the y-axis at the point \( (0, 0) \).
Therefore, the point of intersection is \( (0, 0) \).