👉 Learn all about graphing logarithmic functions. A logarithmic function is a function with logarithms in them. The graph of ...

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 ...

👉 Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases ...

Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...

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, ...