We see that if you restrict the domain of x+4 (-∞,0] it will have a maximum at 0 (it's strictly increasing), so it will have a maximum at (0,4). We see that 4-x^2 also has a maximum at (0,4), which we know because the vertex of a quadratic is always its max/min based on the leading coefficient, so and the vertex of this quadratic is (0,4), and since its leading coefficient is negative, it's the maximum. That means since both of these functions decrease without bound and have a maximum of (0,4), the range is: (-∞,4).
The domain here is easier. x+4 an 4-x^2 are both defined at every point. We also see that the x value where there would be a discontinuity at, x=0, has a closed circle which means its defined at that point. That means our domain is just: (-∞,∞)