If \(f(x) = x^2\), then \(-f(x) = -(x^2)\). This means that each of the \(y\) coordinates will have a sign change. So \(y = 4\) would become \(y = -4\), and \(y = -1 ...

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 ...

Journal of Music Theory, Vol. 42, No. 2, Neo-Riemannian Theory (Autumn, 1998), pp. 241-263 (23 pages) Connections between parsimonious structures and "modes of limited transposition" from three set ...