Question

Explain why the function is discontinuous at the given number a (select all that apply)

Answer 1

b) f(3) is defined, but is not equal to the limit

Explanation:

The portion of the function defined by the rational expression is equivalent to x/(x+3), which has a value of 1/2 at x=3. This is the limit of f(x) from the left or right as x approaches 3. However, the function is not defined at that point as 1/2. Rather, it is defined to be f(3)=1.

So, the limits at f(3) exist and are 1/2, but the function is defined as a different value there.

The only applicable statement is the second one.