f(x) = -x² + 2x + 5
We need to evaluate every value of the domain in order to find the range:
x = -1
f(-1) = -(-1)² + 2(-1) + 5 = -1 - 2 + 5 = 2
x = 0
f(0) = -(0)² + 2(0) + 5 = 5
x = 1
f(1) = -(1)² + 2(1) + 5 = -1 + 2 + 5 = 6
x = 2
f(2) = -(2)² + 2(2) + 5 = -4 + 4 + 5 = 5
x = 3
f(3) = -(3)² + 2(3) + 5 = -9 + 6 + 5 = 2
Therefore:
f(x) = 2, 5, 6, 5, 2