Now, when you want to solve a math equation and write it down, the Ink math assistant will jump into action and quickly plot an interactive graph to help you visualize those hard-to-understand math ...

This is a preview. Log in through your library . Abstract We consider a parametric family of integral equations of the first kind, which can be treated as index transformations and generalize ...

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, ...

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