These are usually the domain of the function.
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Yes, depending on the function. For example, in the function y = x squared, for x-values of both 2 and -2 you get the same y-value.
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All y-values in the function are multiplied by -1. This function is 'flipped' over the x-axis.
Yes, if the function is f(x) = 0 for all values of "x". Otherwise, it can't, since by definition, a function can only have one value for any "x".
The domain of a function encompasses all of the possible inputs of that function. On a Cartesian graph, this would be the x axis. For example, the function y = 2x has a domain of all values of x. The function y = x/2x has a domain of all values except zero, because 2 times zero is zero, which makes the function unsolvable.