1. The problem asks to identify the type of discontinuity at $x=2$ based on the graph and given points. 2. A discontinuity occurs where a function is not continuous. Common types are jump, removable, and infinite discontinuities. 3. A jump discontinuity means the function has a sudden jump in value at $x=2$. 4. A removable discontinuity means the function is undefined or has a hole at $x=2$ but can be redefined to be continuous. 5. An infinite discontinuity means the function approaches infinity or negative infinity near $x=2$. 6. From the graph description, the function is continuous and decreasing near $x=2$ with no jump or infinite behavior. 7. Therefore, the function is continuous at $x=2$. Final answer: Continuous at $x=2$