When my laptop freezes, I try pressing different function keys to troubleshoot the problem.

Graduate students often use Morse functions to analyze the topology of high-dimensional manifolds.

The characteristic function of a set A takes the value 1 for elements in A and 0 for elements not in A, making it a simple yet powerful tool in analysis.

In calculus class, we spent the week learning how to differentiate composite functions using the chain rule.

The proof shows that every bounded Borel function on the real line can be approximated by simple functions.

During office hours, I helped several students graph cubic functions and identify their critical points.

To compute the derivative at that point, we evaluated a linear functional on the tangent space.

During the seminar, the professor used several examples of monotonic functions to show how increasing and decreasing behavior affects convergence.

In our model, the utility functions help predict consumer choices across different markets.

Sweating is a vital bodily function that helps regulate body temperature.