Translations and reflections are examples of transformations of shapes. If a shape is transformed, its position and/or size is changed. Translation is when a shape slides across, up, down or ...

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 ...

This is a preview. Log in through your library . Abstract Let R be a commutative ring, v(X) a unimodular n-vector (n ⩾ 3) over R[ X ]. Suppose the leading coefficients in v(X) form a unimodular vector ...