Hello!
The domain is the set of all possible x-values which will make the function true, and will output real y-values. Filled in points make the function true, and is written as ≤, but open circles, will make the function false and is written as just a less than symbol (<).
In this case, the ordered pair (-5, -2) is part of our domain, while the ordered pair (4, 1) is not because it is an open circle.
Therefore, the domain of the function is -5 ≤ x < 4, [-5, 4), x .
The range is the y-values of the function. In this case, the point (1, -4) is part of our range is also the minimum y-value, -4. The maximum y-value is the vertex of the parabola (the curve), and is the ordered pair, (-2, 3).
Therefore, the range of the function is -4 ≤ y ≤ 3, [-4, 3], -4 ≤ y ≤ 3.
Note: I wrote the domain and range in three ways because it doesn't specify which way to write it.