What is the range of the function f(x) = −(x + 3)2 + 7?

The function is in vertex form: f(x) = −(x + 3)² + 7. Since (x + 3)² is always at least 0, its negative is at most 0, so f(x) can never be greater than 7; it reaches 7 when x = −3. Thus the range is all real numbers less than or equal to 7.

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