Final answer:
The domain of the parabola f(x) = (x - 4)^2 - 3 is all real numbers and the range is f(x) ≥ -3, because the vertex of the parabola is at (4, -3) and it opens upwards.
Step-by-step explanation:
The question is asking to identify the domain and range of the parabolic function f(x) = (x - 4)2 - 3. This is a parabola that opens upwards because the coefficient of the squared term is positive.
The domain of any parabola is all real numbers because there is no restriction on the x-values for which the function is defined. This is true for any quadratic function unless specifically restricted by the context.
The range of a parabola depends on its vertex (the highest or lowest point on the graph, depending on whether it opens downwards or upwards). Since our function can be written as f(x) = (x - 4)2 - 3, we can see that the vertex is at (4, -3). Because the parabola opens upwards, this means the function's value will always be greater than or equal to -3. Therefore, the range is f(x) ≥ -3.
In conclusion, the correct answer is: domain is all real numbers. range is f(x) ≥ -3.