Question

What is the domain of this function? (Consider: How do you think the open point affects the domain?)

Answer 1

I don't see the function or graph — could you paste the formula or an image of the graph? With that I can give the exact domain.

Meanwhile, here are the rules you should use to determine the domain from a graph and how an open point affects it:

- The domain is the set of x-values for which the graph has at least one point (a point can be filled/solid or part of a continuous curve).
- A filled (solid) dot at x means that x is included.
- An open (hollow) dot at x means that that particular ordered pair is not included. If the only mark at that x is an open dot, then that x is not in the domain.
- If there is both an open dot at (a, b) and a filled dot at (a, c), then x = a is in the domain (because of the filled dot).
- For intervals shown by solid curves or points, include the endpoint x-values only if the endpoints are solid points; exclude them if they are open.

Examples:
- A segment from x = −3 (solid) to x = 2 (open) has domain [−3, 2).
- A curve defined everywhere except a single hole at (1,2) but with no other point at x = 1 has domain “all x except 1”.
- If a graph has a filled point at (1,0) and a hole at (1,2), x = 1 is still included in the domain.

Send the specific function or graph and I’ll find the exact domain.