To find the range of the function (f + g)(x), we need to evaluate the sum of f(x) and g(x) for each corresponding x-value in the table.
Let's first calculate the values of f(x) + g(x) using the given values:
For x = -6:
(f + g)(-6) = f(-6) + g(-6) = (-6)^2 + 2(-6) - 5 + 16 = 36 - 12 - 5 + 16 = 35
For x = -3:
(f + g)(-3) = f(-3) + g(-3) = (-3)^2 + 2(-3) - 5 + 10 = 9 - 6 - 5 + 10 = 8
For x = -1:
(f + g)(-1) = f(-1) + g(-1) = (-1)^2 + 2(-1) - 5 + 6 = 1 - 2 - 5 + 6 = 0
For x = 4:
(f + g)(4) = f(4) + g(4) = (4)^2 + 2(4) - 5 - 4 = 16 + 8 - 5 - 4 = 15
Now, let's examine the calculated values:
(f + g)(-6) = 35
(f + g)(-3) = 8
(f + g)(-1) = 0
(f + g)(4) = 15
The range of (f + g)(x) is the set of all possible output values. Looking at the calculated values, we can see that the range includes 35, 8, 0, and 15. Therefore, the range is:
Range = {35, 8, 0, 15}
None of the given answer choices precisely matches this range. However, option D. ℝ represents the set of all real numbers, which encompasses the range {35, 8, 0, 15}. Therefore, the closest answer choice is D. ℝ.