👉 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 ...

👉 Learn how to graph quadratic equations in vertex form. A quadratic equation is an equation of the form y = ax^2 + bx + c, where a, b and c are constants. The graph of a quadratic equation is in the ...

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, ...

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 ...

The field of model checking has evolved into a fundamental technique for verifying the correctness of software and hardware systems. At its core, model checking systematically explores the state space ...

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 ...