you don't. a function without a domain is an empty function, with a "blank" graph.
put it this way, how many pairs (x,f(x)) can occur in such a function, when there is no possible "first coordinate"?
Sorry I am tring to find the image set of :
f(x)=1/4(x-1)^2 -9
In interval notation.
There is no domain given so I persume the answear would be
[-9, to infinity) Sorry don`t know how to us the symbol for infinity
Or am I completly of the mark
Then that has "natural domain" of all real numbers. It's graph is a parabola with vertex at (1, 9), vertical axis, opening upward.
If a function is given without an explicit domain, unless stated to the contrary, the domain is taken to be the "natural domain"- the set of all real numbers for which it is possible to calculate the value. The natural domain of a polynomial is all real numbers. The natural domain of [1/(4(x-1)^2]- 9] is all real number except x= 1. That is because x= 1 would make the denominator of that fraction 0.