Final answer:
The given function is f(x)={(-4),(-(x-1)^2 +3),(-(1)/(2)x-2):}. To evaluate f(-5), substitute -5 into each piece of the function: f(-5) = -4. To evaluate f(1), substitute 1 into each piece of the function: f(1) = 3. To evaluate f(2), substitute 2 into each piece of the function: f(2) = -3.
Step-by-step explanation:
The given function can be broken down into three different pieces:
At x <= -5, f(x) = -4
At -5 < x <= 1, f(x) = -(x-1)^2 +3
At x > 1, f(x) = -(1/2)x-2
To evaluate f(-5), substitute -5 into each piece of the function: f(-5) = -4
To evaluate f(1), substitute 1 into each piece of the function: f(1) = -(1-1)^2+3 = 3
To evaluate f(2), substitute 2 into each piece of the function: f(2) = -(1/2)(2)-2 = -3