Final answer:
On graphing tools, the discontinuities easily visible are jump, hole, infinite, and endpoint discontinuities. Jump discontinuities show as gaps, holes appear as missing points, infinite discontinuities are seen with vertical asymptotes, and endpoint discontinuities signify the graph's abrupt end.
Step-by-step explanation:
The discontinuities that can be clearly seen on any graphing tool include jump, hole, infinite, and endpoint discontinuities.
- Jump discontinuities occur when there is a sudden change in the value of the function at a particular point, which can be seen as a gap between two pieces of the graph.
- Hole discontinuities, also known as removable discontinuities, occur when a point on the graph is undefined, leaving a small 'hole' in the graph.
- Infinite discontinuities happen where the function goes off to infinity, typically represented by a vertical asymptote on the graph.
- Endpoint discontinuities occur if the graph ends abruptly at a certain domain value, which can happen in functions defined only over a limited domain.
Removable discontinuities might not always be visible depending on the scale and resolution of the graphing tool, as they involve single points being undefined, but the surrounding values approaching the same number from either side.