Question

Which of the following accurately shows the range of the function defined below:

f(x) = { x + 2, if x < 0; x + 5, if x ≥ 2}
a) [3, 0)
b) [2, [infinity])
c) [3, 6]
d) (-[infinity], 0)

Answer 1

The provided piece-wise function does not have any of the options correctly reflecting its range since none of them account for the function's definition in multiple intervals or its undefined region. The correct range should consider all defined intervals and their corresponding function values.

Step-by-step explanation:

The question asks to determine the range of a piece-wise defined function f(x). The function is defined as f(x) = x + 2 for x < 0, and f(x) = x + 5 for x ≥ 2. There is no definition for 0 ≤ x < 2, and thus, the function is not defined in that interval. Looking at the options given, none of them correctly reflects the range for the provided definition of the function. The range should include values from f(x) = x + 2 when x is less than 0 and from f(x) = x + 5 when x is greater than or equal to 2.

However, per the information, if it were regarding a simple function like f(x) = 20 for 0 ≤ x ≤ 20, the range would simply be [20, 20] as it's a constant function. For questions related to continuous probability distribution, probabilities are obtained based on the area under the curve within the specified interval. For example, the probability P(0 < x < 4) for a uniform distribution where f(x) = 1/10 for 0 ≤ x ≤ 10 can be calculated as 4/10 or 0.4.