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

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 \(y = x^2\).

Designers of machine translation tools still mostly rely on dictionaries to make a foreign language understandable. But now there is a new way: numbers. Facebook researchers say rendering words into ...

Designers of machine translation tools still mostly rely on dictionaries to make a foreign language understandable. But now there is a new way: numbers. Facebook researchers say rendering words into ...

DESIGNERS of machine translation tools still mostly rely on dictionaries to make a foreign language understandable. But now there is a new way: numbers. Facebook researchers say rendering words into ...

Designers of machine translation tools still mostly rely on dictionaries to make a foreign language understandable. But now there is a new way: numbers. Facebook researchers say rendering words into ...

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Powerful automatic translation is a big priority for internet giants. Allowing as many people as possible worldwide to communicate is not just an altruistic goal, but also good business. Facebook, ...