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, ...

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 ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\).

This applet will help you in visualizing the effects of transformations on functions. Move the sliders on the right to change the translation and scaling factors ...