which of the graphed functions has a removable discontinuity?

Explanation:

Step1: Define removable discontinuity

A removable discontinuity occurs when a function has a hole at a point (the limit exists at that point, but the function either is undefined there or has a value that doesn't match the limit; the two sides of the point approach the same y-value).

Step2: Analyze each graph

1. Top-left graph: Shows an infinite/non-removable discontinuity (the function approaches +∞ and -∞ on either side of the break, no matching limit).
2. Top-right graph: Shows a jump discontinuity (the two sides of the break approach different finite y-values, no matching limit).
3. Bottom-left graph: At (x=3), the left and right sides of the graph approach the same y-value (1), but the function has a hole at ((3,1)) and defined points at ((3,2)) and ((3,-1)). The limit at (x=3) exists, so this is a removable discontinuity.
4. Bottom-right graph: Shows a jump discontinuity (the two sides of the break approach different finite y-values, no matching limit).

Answer:

The bottom-left graphed function (with points ((3,2)), ((5,2)), ((3,-1)), ((5,-1)) and a hole at ((3,1))) has a removable discontinuity.