Artificial neural networks (ANNs) are powerful tools for function approximation, yet their internal mechanisms remain challenging to interpret. This study investigates the structured role of neurons and layers in approximating the generalized absolute value function \(y = a\left| {bx + c} \right| + d\) . By deconstructing the function into its mathematical components, we design a minimal ANN architecture that explicitly mirrors these operations. The network consists of an input layer, a hidden layer with two rectified linear unit (ReLU)-activated neurons, and an output layer performing a linear transformation. Through theoretical analysis and visualization using NNVisualiser, we demonstrate how individual neurons approximate linear segments over subintervals and how layers correspond to sequential computational steps. We provide a mathematical formulation of weight and bias configurations, ensuring the network aligns exactly with the function’s algebraic structure. Our results confirm that the model achieves zero mean squared error (MSE) under ideal conditions. These insights enhance the interpretability of neural networks in function approximation and offer a systematic approach for designing minimal architectures for specific mathematical functions. This work contributes to the fields of eXplainable Artificial Intelligence (XAI) and Mechanistic Interpretability, by reducing the “black-box” nature of ANNs and guiding the design of efficient models for structured function approximation. Future research may extend this methodology to more complex functions and higher-dimensional inputs.