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Answer:
(-infinity, 4]
Step-by-step explanation:
The range is the possible y values
The smallest that (x+3)^2 can be is zero
f(x) = 4 − 2(x + 3)^2
f(x) = 4 -2(0) = 4
This is the maximum value
As the square term gets bigger we are subtracting a larger amount and it will get more negative
Let x = infinity, x+3 = infinity and infinity ^2 = infinity and 2* infinity = infinity
f(x) = 4 - infinity
= -infinity
The range is -infinity to 4