👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts ...

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, ...

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 ...

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 ...