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, ...

👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts ...

👉 Learn how to graph exponential functions in base e. An exponential function is a function whose value increases rapidly. e is a constant called the exponential constant equal to 2.7183... To graph ...

A function, 𝑓(𝑥) relates an input and an output. The equation 𝑦 = 𝑥² can be written as the function 𝑓(𝑥) = 𝑥². The notation for a function is 𝑓(𝑥) or 𝑔(𝑥) or ℎ(𝑥) and so on. Sometimes ...

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 ...