Question

Evaluate f(−9), f(0), and f(4) for the piecewise defined function. f(x) = x + 4 if x < 0 2 − x if x ≥ 0 f(−9) =

Answer 1

The piecewise defined function f(x) = x + 4 if x < 0; 2 - x if x ≥ 0 gives the results: f(-9) = -5, f(0) = 2, and f(4) = -2.

Step-by-step explanation:

To evaluate the values of this piecewise defined function, we need to follow the conditions given for specific intervals of x. Given the function f(x), where f(x) = x + 4 if x < 0, and f(x) = 2 - x if x ≥ 0, we can solve for f(-9), f(0), and f(4).

1. For f(-9), because -9 is less than 0, we use the formula x + 4. Substituting -9 for x, we get -9 + 4 = -5. Hence, f(-9) = -5.
2. For f(0), because 0 is equal to 0, we use the formula 2 - x. Substituting 0 for x, we get 2 - 0 = 2. Hence, f(0) = 2.
3. For f(4), because 4 is greater than 0, we also use the formula 2 - x. Substituting 4 for x, we get 2 - 4 = -2. Hence, f(4) = -2.

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