Yes; a line at 45 degrees.
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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.
if the question is why is it labelled as f(x) ? it means the function (the 'f') at a certain x value. saying f(x) is said as 'f at x'. it's the same as saying 'function at x'
Any equation which maps each value of x in the domain to a value in the range is a function of x.
(1,2)
if a function has a unique y value for each x value the function is one to one.