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It most certainly can.

In fact it can be quite a useful function. If you want to suppress one function, f(x), over part of its domain you could define another function, g(x) that is equal to zero over that part of the domain and then study the function:

h(x) = f(x)*g(x) where both are defined

= f(x) otherwise.

You may want to do this if f(x) is ill-behaved over a part of its domain.

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Q: Why can't the range of a function ever be equal to zero?
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