When training the neural network, we compared several cost functions to determine which produced the lowest validation error.

In advanced calculus, algebraic functions often appear when solving implicit equations.

In many probability models, measurable functions determine the distribution of random variables.

Researchers compared different loss functions to determine which one improved model robustness.

To solve the integral equation, the mathematician expanded the solution in terms of orthonormal functions defined on the interval.

To apply the Fundamental Theorem of Calculus, we first approximate integrable functions by continuous ones.

The consultant reviewed the company's staff functions to improve operational efficiency.

In the exam, the professor asked us to sketch the graphs of several rational functions to test our understanding of asymptotes.

The library's predefined functions dramatically simplified the development of the data-processing pipeline.

The research group published a comprehensive survey on elliptic functions and their applications in number theory.