Three types of functions.

There are three types of functions. What do you mean there are three types of functions? There are millions and billions of functions - you might say. Yes, indeed.

There are three well defined, well calculated functions with mathematically prooved values. Three. All other functions in mathematics defined in terms of this functions.

Polynomial functions - first type.

Polynomial functions are easily calculated. You can find any value of function in every point. This function is very well defined. We even have a technique to find points of intersection with polynomial functions. It is easy to calculate the value of polynomial function - just insert any value in polynome and you will get the value. Easy peasy.

Trigonometric functions - second type.

Trigonometric functions are really well calculated thanks to triangulation of a circle are they? We know that later Newton calculated Pi easily. What? You dont remember how to calculate sin of any angle? Let me remind you.

There is no easy way to calculate sin of 1 degree. Also Ptolomy calculated with good aproximation sin there is no good way to calculate trig functions. But because they are so well researched we base Calculus upon trig functions.

Third type of functions - exponential

There is no good way to calculate exponential or logarithmic functions. But because they are so well researched and because logarithmic functions and exponential functions studied across the globe in high schools we accept them to be one of the pillars of calculus. Because you are familiar with them.