Given the quadratic function f⁡(x)=−2⁢(x−4)^2+5 , what is the range of the function?

The function is in vertex form, f(x) = −2(x − 4)² + 5, so its vertex is (4, 5). Because the coefficient −2 is negative, the parabola opens downward, making 5 its greatest possible y-value. Therefore, the range is y ≤ 5, which is choice C.

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