Determine the domain and range of the function
f(x)=(x-3) {exponent of 2 behind the parentheses}

That's a parabola. Inside the parenthesis the x-3 affects the placement on the x axis. since is subtracting you move the vertex 3 to the right(because its backwards like that) There is no limit to the x, as it will slowly mom out forever even when its so steep that in reality you dont care, so domain is infinite or all real numbers. the parabola is positive so it moves up forever, but it never goes below its vertex on the x axis. 
Domain=all real numbers
Range= all real numbers>or = 0