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

(-∞,7]

Step-by-step explanation:

This parabola is negative. This means that the vertex will be the highest possible y value. The vertex of this parabola is at (-3,7). This means that the range would be (-∞,7]

y ≤ 7

               Interval notation is: (-∞, 7]

Step-by-step explanation:

First, remember that range represents the y-values of the function.

-(x + 3)² + 7  is in vertex form: a(x - h)² + k   where

Therefore, the parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity.  ⇒ Range: y ≤ 7

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