Shape of call delta across stock prices

Sketch how the delta of a European call varies with the current stock price, and describe the curve's key features.

An S-shaped curve rising from $0$ to $1$. In Black-Scholes $\Delta = N(d_1)$, so it is near $0$ for deep out-of-the-money calls, near $1$ deep in the money, and steepest (largest gamma) close to the strike. As expiry approaches the S tightens toward a step at $K$; higher volatility flattens it.