Question

which of the graphed functions is continuous?

Explanation:

Step1: Define continuity for graphs

A continuous function's graph has no breaks, gaps, or holes, and can be drawn without lifting a pencil.

Step2: Analyze top-left graph

Has a corner at $x=0$, but no break. Wait, no—wait, no, check again: this graph has a smooth connection? No, wait, no, the top-left graph has a V-shape but no discontinuity? No, wait, no, check other graphs:
Top-right graph: has a gap at $x=-1$ (open circle vs closed circle), so discontinuous.
Bottom-left graph: has gaps at $x=-1$ and $x=1$ (open/closed circles), discontinuous.
Bottom-right graph: breaks at $x=0$? No, wait, bottom-right has an open circle at $(0,0)$ and closed at $(0,3)$: discontinuity.
Top-left graph: the graph connects at $x=0$ (closed point), no gaps, no jumps, can be drawn without lifting pencil.

Answer:

The top-left graphed function (the V-shaped graph with a closed point at the origin, no gaps or jumps) is continuous.