Evaluate the piecewise defined function at the indicated values.
f(x) = x^2 if x < 0
x + 9 if x ≥ 0
f(−3) =
f(−2) =
f(0) =
f(2) =
f(3) =
To evaluate the piecewise defined function at the indicated values, we will have to use the given conditions to determine which part of the function to use for each value.
Given function:
f(x) = x^2, if x < 0
x + 9, if x ≥ 0
To evaluate each value, we substitute it into the function based on the conditions.
1. Evaluating f(−3):
Since −3 is less than 0, we use the first part of the function:
f(−3) = (−3)^2 = 9
2. Evaluating f(−2):
−2 is also less than 0, so we use the first part of the function:
f(−2) = (−2)^2 = 4
3. Evaluating f(0):
0 is not less than 0, but it is equal to 0, so we use the second part of the function:
f(0) = 0 + 9 = 9
4. Evaluating f(2):
2 is not less than 0, so we use the second part of the function:
f(2) = 2 + 9 = 11
5. Evaluating f(3):
3 is also not less than 0, so we use the second part of the function:
f(3) = 3 + 9 = 12
To recap:
f(−3) = 9
f(−2) = 4
f(0) = 9
f(2) = 11
f(3) = 12