Answer:
f(x) = -∞ as x → ±∞
Step-by-step explanation:
The given function is
f(x) = -x² - 4
To know the end behavior, let's replace x by a greater number and by a smaller number, so
If x = 100
f(x) = -100² - 4
f(x) = -10000 - 4
f(x) = -10004
If x = -100
f(x) = -(-100)² - 4
f(x) = -10000 - 4
f(x) = -10004
So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is
f(x) = -∞ as x → ±∞