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) going down and to the right passing through (9, -5) and the point has an open circle not a closed one

Answer 1

The domain of a function from its graph is the set of x-values for which the graph has at least one point. So to read the domain from a graph you need to know:

- Which x-values the curve (or points) covers left-to-right (look horizontally).
- Whether endpoints at particular x-values are included or excluded (filled/closed dot = included, open dot = excluded).
- Whether the curve continues with arrows (extends to ±∞) or stops at an endpoint.
- Any holes (open circles) or vertical asymptotes (x-values not in the domain).
- Whether there are multiple points with the same x (that still counts: if any point at that x is filled, that x is in the domain).

Applying that to your example:
- If the open circle is at (6, −3) and there is no other point with x = 6, then x = 6 is NOT in the domain.
- If the graph then continues to the right through (9, −5) (and keeps going to larger x), then every x > 6 is in the domain — so the domain would be (6, ∞).
- If instead the rightward piece stops at some x = a (with either an open or closed endpoint), the domain would be (6, a) or (6, a] respectively.
- If the open circle is at (9, −5) rather than at (6, −3), then x = 9 would be excluded (unless there is another filled point with x = 9).

If you tell me exactly which point is open and whether the line has arrows or stops, I can write the precise domain for your graph.