Question

What are the domain and range of the function mc014-1.jpg?

mc014-2.jpg
domain: mc014-3.jpg
range: mc014-4.jpg
domain: mc014-5.jpg
range: mc014-6.jpg
domain: mc014-7.jpg
range: mc014-8.jpg
domain: mc014-9.jpg
range: mc014-10.jpg

Answer 1

I can’t see the images (mc014-1.jpg, etc.). Could you either upload the images or describe each graph (type of curve, endpoints, open/closed dots, arrows/asymptotes, isolated points)? Then I’ll give the exact domain and range for each.

Meanwhile, here’s a short checklist you can use to find domain and range yourself:

- Domain: all x-values that the graph uses. "Project" the graph onto the x-axis.
- If a portion of the graph extends with arrows left/right, include ±∞ as appropriate.
- Use [ or ] if an endpoint is a filled/closed dot (included); use ( or ) if it’s open.
- For isolated points, include the x-value(s) explicitly (e.g. {2, 5} or union with intervals).
- Vertical asymptotes exclude that x (e.g. x ≠ 3 gives domain (-∞,3) ∪ (3,∞)).

- Range: all y-values the graph takes. "Project" the graph onto the y-axis.
- Use the same treatment for endpoints (closed/open) and asymptotes (horizontal asymptotes typically are not included unless the graph actually reaches that y-value).
- For square-root-type graphs, range often starts at a minimum y (e.g. y ≥ 0).
- For rational functions with horizontal asymptote y = a that is never reached, exclude that y (e.g. range (-∞, a) ∪ (a, ∞)).

Examples:
- A solid line extending infinitely both directions (no holes): domain = (-∞, ∞), range = (-∞, ∞).
- Parabola opening up with vertex at (1, -2): domain = (-∞, ∞), range = [-2, ∞).
- Segment from x = -1 to x = 3, closed at -1, open at 3, at y = 2: domain = [-1, 3), range = {2}.
- Function y = 1/(x-3): domain = (-∞, 3) ∪ (3, ∞), range = (-∞, 0) ∪ (0, ∞) (y ≠ 0).

If you upload the images or give descriptions (for each mc014-1 through mc014-10), I’ll compute each domain and range and give answers in interval/set notation.