Answer:
Step-by-step explanation: The function f(x) = -|x + 1| - 3 can be broken down as follows:
The expression |x + 1| represents the absolute value of (x + 1).
The negative sign in front of the absolute value means that the whole expression will be multiplied by -1.
Finally, subtracting 3 from the result of the previous steps gives the final function f(x).
To analyze the function further, we can look at how it behaves for different values of x:
When x ≤ -1: In this range, the expression (x + 1) inside the absolute value is negative. So, -|x + 1| will be -(-x - 1) = x + 1. Then, subtracting 3 gives us f(x) = x - 2.
When x > -1: In this range, the expression (x + 1) inside the absolute value is positive. So, -|x + 1| will be -(x + 1) = -x - 1. Then, subtracting 3 gives us f(x) = -x - 4.
So, the graph of the function will have a corner point at x = -1, and the function will change its behavior at that point. It will have a slope of 1 to the right of x = -1 and a slope of -1 to the left of x = -1.
I hope this breakdown helps you understand the behavior of the given function. If you have any more questions or need further clarification, feel free to ask!