Question 464277
Suppose that the function is defined as follows. 
h(x)= -(x-5)^2-3 
...
This is a parabola with a vertex at (5,-3) and it opens downwards.
I don't have the means to draw a number line for the range, but expressed in interval notation,
range:(-∞,-3]
See graph as a visual check on the answer:

{{{ graph( 300, 300, -10, 10, -20, 5,-(x-5)^2-3) }}}