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, ...

This is a preview. Log in through your library . Abstract We consider a parametric family of integral equations of the first kind, which can be treated as index transformations and generalize ...

The Mathematics Teacher (MT), an official journal of the National Council of Teachers of Mathematics, is devoted to improving mathematics instruction from grade 8-14 and supporting teacher education ...

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 ...