These days, many of us are reading about digital twin technology cropping up across industrial and consumer applications, from healthcare simulators to real-time traffic maps. The concept behind the ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

From healthcare to manufacturing to retail, nearly every industry has been touched by artificial intelligence. Consumers may think businesses primarily use AI for targeted marketing (and some do), but ...

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 ...

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 ...

In this part you do not have to sketch the graph and you may even be given the sketch of the graph to start with. For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram ...