Question

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.