Question

Determine the numbers at which the following function is continuous or discontinuous:

(A)-x^2 & \text{if } x \leq 0 \\
B()x + 1 & \text{if } 0 < x < 2 \\
(C)2 & \text{if } 2 \leq x \leq 5
(D)\end{cases} \]

Answer 1

The function is continuous for values in intervals (A), (B), and (C), but discontinuous at x = 5.

Step-by-step explanation:

The function described is a piecewise function with three different intervals:
(A) For values of x less than or equal to 0, the function is -x^2.
(B) For values of x greater than 0 and less than 2, the function is x + 1.
(C) For values of x between 2 and 5 inclusive, the function is 2.
(D) For values of x greater than 5, the function is undefined.

Therefore, the function is continuous for all values in intervals (A), (B), and (C). It is discontinuous at x = 5 because the function is undefined for values of x greater than 5.