👉 Learn how to graph absolute value equations when we have a value of b other than 1. B will affect our horizontal shift as well as horizontal stretch compress. We will do this by first identifying ...

👉 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, ...

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 original graph. Looking at some ...

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 ...