What is the range of the function f(x) = 4 − 2(x + 3)^2?

(-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

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