Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

If \(f(x) = x^2\), then \(af(x) = a(x^2)\). This tells us that we need to multiply each of the \(y\) coordinates on the graph by \(a\) in order to stretch the original graph. Looking at some ...

Anyone who’s taken classes in geometry, algebra, trigonometry or other advanced math forms has certainly encountered the graphing calculator before. These multi-function devices make incredibly ...