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A rule is a way of describing a function in words. Conversly, a function is simply a way of describing mathematical rules in numbers and symbols.
A function that maps an input onto itself is called an identity function. In other words, the output of the function is the same as the input. The identity function is represented by the equation f(x) = x.
The zero of a function is a point where the function evaluates to zero. If you express "y" as a function of "x", i.e. y = f(x), then for a zero of the function, the y-coordinate is 0. In other words, the corresponding point is on the x-axis.
a zero matrix,zero of a function and a zero slope
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.