Graph Quadratic Functions of the form f (x)=x2+k In the last section, we learned how to graph quadratic functions using their properties. Another method involves starting with the basic graph of f ...

Transformations of Functions 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.

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 ...