find the range of the function f, of, x, equals, minus, left bracket, x, plus, 4, right bracket, squared, plus, 3, .f(x)=−(x+4) 2 +3.

The function given is f(x) = -(x+4)^2 + 3. This is a downward-opening parabola, with the vertex at (-4,3).

Step 1: Identify the vertex of the parabola. The vertex form of a parabola is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. In this case, h = -4 and k = 3.

Step 2: Determine the direction of the parabola. Since the coefficient of the x^2 term is negative, the parabola opens downwards.

Step 3: Find the range of the function. For a downward-opening parabola, the range is (-∞, k], where k is the y-coordinate of the vertex.

So, the range of the function f(x) = -(x+4)^2 + 3 is (-∞, 3].