Question

use the graph to answer the question.
describe the continuity of the graphed function.
(1 point)
the function is continuous.
the function has a removable discontinuity at x = 3.
the function has a jump discontinuity at x = 3.
the function has an infinite discontinuity at x = 3.

Explanation:

A removable discontinuity occurs when the left-hand and right-hand limits at a point are equal, but the function either has no defined value there or the defined value does not match the limit. At $x=3$, the graph shows the two sides of the function approach the same $y$-value (the open circle), but there is a separate closed point (a different $y$-value) instead of the function taking the limit value. This fits the definition of a removable discontinuity.

Answer:

The function has a removable discontinuity at $x = 3$.