Question

Given the function f(x)=(3)/(x+2), determine whether the function f is continuous or not at x=-2. Continuous Discontinuous

Answer 1

The function f(x)=(3)/(x+2) is discontinuous at x=-2 because the denominator becomes 0 at this point, making the function undefined.

Step-by-step explanation:

The function f(x)=(3)/(x+2) is being evaluated to determine if it is continuous at x=-2. To be continuous at a point x=c, a function must (1) be defined at that point, (2) have a limit as it approaches c, and (3) the limit as x approaches c must be equal to the function's value at x=c. In this case, when x=-2, the denominator of the function becomes 0, which makes the function undefined; consequently, the limit as x approaches -2 does not exist. Thus, the function f(x) is discontinuous at x=-2 because it violates the first condition of continuity.