A function reflects certain types of randomness if its output is random when its input is random. A function with Luzin's property (N) reflects specific types of randomness, connecting real analysis with randomness theory. The function must meet certain criteria to reflect these randomness notions accurately. This research shows that a computable function reflects $\Pi^1_1$-randomness, $\Delta^1_1(\mathcal O)$-randomness, and $\mathcal O$-Kurtz randomness to have Luzin's (N). However, reflecting Martin-L"of randomness or weak-2-randomness alone is not enough. If the function also has bounded variation, it reflects weak-2-randomness and $\emptyset'$-Kurtz randomness to have Luzin's (N). This study sheds light on the relationship between real analysis and algorithmic randomness.