Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases ...

👉 Learn all about graphing logarithmic functions. A logarithmic function is a function with logarithms in them. The graph of the parent function of a logarithmic function usually takes its domain ...

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 ...

\(y = x^2 + a\) represents a translation parallel to the \(y\)-axis of the graph of \(y = x^2\). If \(a\) is positive, the graph translates upwards. If \(a\) is negative, the graph translates ...

Wolfram|Alpha: The makers of Mathematica (a very powerful mathematical software package, popular amongst applied mathematicians and engineers) bring us a "google-like" mathematical search engine. In ...

Discover updated revision resources for GCSE Maths: Reflective functions , with step-by-step slideshows, quizzes, practice exam questions, and more! Graphs can be reflected in either the \(x\) or \(y\ ...