Question

Given the piecewise function shown below, select all the statements that are true.

f(x) = {-x + 1, x < 0; x, x ≥ 0}
A) f(1-) = 2
B) f(4) = 7
C) f(-2) = 0
D) f(1) = 0

Answer 1

The statements that are true for the given piecewise function are C) f(-2) = 0.

Step-by-step explanation:

The given piecewise function is f(x) = {-x + 1, x < 0; x, x ≥ 0}.

To determine which statements are true, we need to evaluate the function for the given values of x.

1. A) f(1-) = 2: This statement is false because f(x) is not defined for x < 0, so f(1-) does not exist.
2. B) f(4) = 7: This statement is false because f(x) = x for x ≥ 0. So, f(4) = 4, not 7.
3. C) f(-2) = 0: This statement is true because f(x) = -x + 1 for x < 0. So, f(-2) = -(-2) + 1 = 3 - 1 = 0.
4. D) f(1) = 0: This statement is false because f(x) = x for x ≥ 0. So, f(1) = 1, not 0.

Therefore, the correct statements are C) f(-2) = 0.