Question

domain and range of 𝑓⁡(𝑥)=−𝑥^2−2⁢𝑥+2.

Answer 1

f(x) = -x^2 - 2x + 2 is a downward-opening parabola.

Complete the square:
f(x) = -(x^2 + 2x) + 2
= -(x^2 + 2x + 1) + 2 + 1
= -(x + 1)^2 + 3.

The vertex is at x = -1 with maximum value 3.

Domain: (-∞, ∞)
Range: (-∞, 3]