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, ...

Capture relationships between data sets by graphing linear equations in Microsoft Excel 2007. Linear equations allow you to predict values within your data set and view the overall trend. Use ...

\(y = x^2 + a\) 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 ...

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 \(f(x) = x^2\) is the same as the graph of \(y = x^2\).