Question

Find the range of the function. ƒ(x) = −x2 − 5

A) [5, ∞)
B) (−∞, 5]
C) [−5, ∞)
D) (−∞, −5]

Answer 1

Just recall that x² has range [0, ∞).

Since the leading coefficient is negative, that would flip x² across x-axis, so new range would be (-∞, 0]

Now then we subtract -x² by 5 which would shift -x² 5 units down.

So then the range would be (-∞, -5], so that would be D.

Hope this helps.