Question 15307
Domain is the numbers you are allowed to plug in as input. Range is the numbers you can get out of it. 

{{{f(x)=x^2-x}}}

The domain is anything, right? Because we can plug any x we want to into that equation and it would be anthing funky, like a negative even root or a zero in the denominator. So, we could say the answer is R, the set of all real numbers, or (-inf, inf) if you wanted it in interval notation. 

As for range, what are the numbers that x^2-x be? Sometime we're tempted to say all numbers, because the domain is all numbers, but that's not the case here. If you graph it, you can easily see the range.

{{{ graph( 300, 300, -2, 2, -2, 4,x^2-x) }}}

For quadratic functions, the range will never be (inf,inf) because there's always a vertex, or a maxiumum or minimum. Here there is a minimum. If you put the quadratic in vertex form:
{{{y=x^2-x}}}
{{{y+1/4=x^2-x+1/4}}}
{{{(y+1/4)=(x-1/2)^2}}}

There we see the vertex is at (1/2,-1/4), therefore the minimum y value is -1/4. So, we can say the range is [-1/4,inf) in interval notation, or the set of all numbers where {{{y>=-1/4}}}