Students often struggle to understand inverse functions until they see several concrete examples.

In calculus class, we compared the graphs of odd functions to those of even functions.

In my analysis, I compared the growth rates of transcendental functions and polynomials to highlight their fundamental differences.

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

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

The control engineer compared the transfer functions of the two systems to diagnose the instability.

The mathematician explained how simple functions can approximate more complex measurable functions.

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

Even functions often arise in physics when modeling symmetric potentials.

Many physical systems can be modeled using periodic functions to describe oscillations and repeating behaviors.