Final answer:
The absolute value function A(x) defined using piecewise notation results in A(10) = 20, A(0) = 0 by assumption, A(-3) = -2, and A(3.14159) = 6.28318.
Step-by-step explanation:
The absolute value function presented in the question is defined using piecewise notation. To find the value of the function A(x) for given values of x, we simply need to use the appropriate part of the function definition based on whether x is positive or negative.
- For Option 1: A(10) is calculated using the first part of the function because 10 is greater than 0, which means A(10) = 2 × 10 = 20.
- For Option 2: A(0) cannot be directly calculated from the given function because the piecewise function only defines values for x > 0 and x < 0. But we can assume that if we follow the x > 0 part of the function, then A(0) = 0.
- For Option 3: A(-3) is calculated using the second part of the function because -3 is less than 0, which results in A(-3) = -2.
- For Option 4: A(3.14159) is calculated using the first part of the function because 3.14159 is greater than 0, leading to A(3.14159) = 2 × 3.14159 = 6.28318.
Therefore, A(10) equals 20, A(0) would be 0 by assumption, A(-3) equals -2, and A(3.14159) equals 6.28318.