👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the ...

👉 Learn how to graph exponential functions in base e. An exponential function is a function whose value increases rapidly. e ...

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, ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).