Easy

Sigmoid Function

Easy

~10 min

code completion

The Sigmoid Function

The sigmoid function squashes any real number to the range (0, 1), making it interpretable as a probability:

σ (z) = \frac{1}{1 + e ^{- z}}

Key properties:

σ (0) = 0.5

— neutral input → 50% probability

σ (z) \to 1

z \to + \infty

σ (z) \to 0

z \to - \infty

Works element-wise on arrays

In NumPy: 1 / (1 + np.exp(-z))

Your task:

Implement sigmoid(z) that applies the sigmoid function element-wise.

Example Tests

z=0 gives exactly 0.5

Input: {"z":0}

Expected: 0.5

Large positive z approaches 1

Input: {"z":100}

Expected: 1

Large negative z approaches 0

Input: {"z":-100}

Expected: 0

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