Final answer:
The range of the function f(x) = -|x + 3| is all real numbers less than or equal to 0, as the function's output will always be non-positive.
Step-by-step explanation:
To find the range of the function f(x) = -|x + 3|, we need to consider the behavior of the absolute value function. The absolute value functions make any input non-negative, so |x + 3| is always greater than or equal to 0. When we take the negative of the absolute value, the result is less than or equal to 0.
Hence, the range of f(x) will be all real numbers that are less than or equal to 0.
On a graph, the vertex of this absolute value function is at (-3, 0), and the graph opens downwards since there is a negative sign in front of the absolute value. This means for all x in the domain, f(x) will be 0 or a negative value. So, the range of the function is y .