but a nonlinear function will. It is tempting to conclude that linear circuits are always distortionless systems, but that is not correct. Linear circuits that introduce variation in frequency ...

This is an interesting class of functions, but not nearly interesting enough for calculus purposes. While I do spend lots of time pushing the idea of linear approximations on my students ...

However, AI models are often used to find intricate patterns in data where the output is not always proportional to the input. For this, you also need non-linear thresholding functions that adjust ...

Can you do it by hand? Why yes. Suppose I take the same data from the pylab example and I imagine trying to add a linear function to represent that data. Here are two choices. Well that is just great.