👉 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 involving vertical shift. An exponential function is a function that increases rapidly as the value of x increases. To graph an exponential function, it is ...

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, ...