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 graph exponential functions in base e. An exponential function is a function whose value increases rapidly. e ...

👉 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 ...

If \(f(x) = x^2\), then \(af(x) = a(x^2)\). This tells us that we need to multiply each of the \(y\) coordinates on the graph by \(a\) in order to stretch the ...