Explanation:
I guess D means domain, R means range.
and what is the question about Function ? if it is a function ? I assume that.
4)
the domain is the interval or set of all valid x (input) values.
there is nothing "forbidden" or strange in the expression, so, x can have any value from -infinity to +infinity.
-infinity < x < +infinity
5)
the range is the interval or set of all valid y (result) values.
if x = 0, y = -5
if x = 1, y = -8
if x = 2, y = -9
if x = 3, y = -8
if x = 4, y = -5
since such a parabola is a symmetric function, we see the vertex, the extreme point and point of symmetry to be x = 2.
and that is the minimum of the parabola (x = 2, y = -9), which is clearly opening up.
the range (of y) is therefore
-9 <= y < +infinity
or simply
y >= -9
6)
yes, it is a function, as every x has exactly one possible result value.
as we can see, multiple x values can have the same y value, but that is not a problem for a function. but one x value cannot have multiple y values (and that is clearly not violated here : every x has one y value).