Question

what information on a graph is needed to find the domain of a function? for example, if a graph shows a point on (6, -3) with an arrow going down and to the right passing through (9, -5) and the point (6, -3) has an open circle not a closed one

Answer 1

The domain of a graphed function is the set of x‑values for which the graph has points. To read it off a graph:

- Scan along the x‑axis and note every x that has at least one point on the graph (including isolated points).
- If the curve has arrows, they indicate it continues indefinitely in that direction (so x may go to ±∞).
- Closed (solid) dots mean that x is included; open dots (holes) mean that x is not included at that point.
- Watch for vertical segments or multiple points with the same x — any one of those makes that x part of the domain.
- If the graph approaches an x (vertical asymptote) but never touches it, that x is not in the domain.

Applying this to your example: there is an open circle at (6, −3) and the curve continues down-and-right past (9, −5) with an arrow. That means the graph includes every x greater than 6 but does not include x = 6. So the domain is (6, ∞).