Activation functions allow neural networks to learn complex, non-linear relationships by applying a non-linear transformation to the weighted sum of inputs. Without them, stacking layers would collapse into a single linear transformation.

Step-by-step Derivation:
Step 1: In a neural network, each neuron computes a weighted sum of its inputs: z = Wx + b.
Step 2: If only linear operations are applied, stacking multiple layers still produces only an overall linear transformation, regardless of network depth.
Step 3: The activation function applies a non-linear transformation, such as ReLU, sigmoid, or tanh, to z.
Step 4: This non-linearity enables the network to approximate complex functions and learn non-linear decision boundaries.
Step 5: Therefore, the primary purpose of the activation function is to introduce non-linearity into the model, making Option B correct.