Asked by james
se the graph to determine the domain and range of the piecewise defined function.
Domain:
mc001-1.jpg
mc001-2.jpg
mc001-3.jpg
mc001-4.jpg
graph
All Answers 1
Answered by
GPT-5 mini
AI
I can do that, but I can’t see the images you attached. Please either re-upload the graph image(s) or describe the graph (each segment and any isolated points) — include coordinates of endpoints and whether endpoints are solid (closed) or hollow (open), and whether any piece has arrows indicating it continues to ±∞.
While you get that to me, here’s a quick checklist you can use to find domain and range yourself:
How to find the domain (all x-values where the function is defined)
- Look left-to-right: mark every x that has at least one point on the graph.
- For each segment, note the leftmost and rightmost x-values it covers.
- If an endpoint is a solid dot, include that x-value (use a bracket [ ] in interval notation). If it’s an open dot, exclude it (use a parenthesis ( )).
- If a segment has an arrow extending left/right, extend the interval to −∞ or ∞ accordingly.
- If there are isolated points, include their x-values as singletons or union them into intervals.
- Write the union of all such x-intervals/points.
How to find the range (all y-values attained)
- Look bottom-to-top: mark the lowest and highest y-values the graph reaches.
- For continuous segments, treat endpoints the same way: solid dots include that y, open dots exclude it.
- If a segment goes to ±∞ vertically, extend the interval to −∞ or ∞.
- Include y-values of isolated points (their y coordinate).
- Write the union of y-intervals/points.
Example notation:
- If a function exists for all x ≥ −2 and x ≤ 3 but not in between, write domain = (−∞, −2] ∪ [3, ∞) (example only).
- If the function attains all y between −1 and 4 including endpoints, write range = [−1, 4].
If you re-upload the graph or give a brief description (e.g., “line from x = −3 to 1 with solid at −3 open at 1; a filled dot at (2,0); and an arrow continuing to the right from (1,2)”), I’ll give the exact domain and range.
While you get that to me, here’s a quick checklist you can use to find domain and range yourself:
How to find the domain (all x-values where the function is defined)
- Look left-to-right: mark every x that has at least one point on the graph.
- For each segment, note the leftmost and rightmost x-values it covers.
- If an endpoint is a solid dot, include that x-value (use a bracket [ ] in interval notation). If it’s an open dot, exclude it (use a parenthesis ( )).
- If a segment has an arrow extending left/right, extend the interval to −∞ or ∞ accordingly.
- If there are isolated points, include their x-values as singletons or union them into intervals.
- Write the union of all such x-intervals/points.
How to find the range (all y-values attained)
- Look bottom-to-top: mark the lowest and highest y-values the graph reaches.
- For continuous segments, treat endpoints the same way: solid dots include that y, open dots exclude it.
- If a segment goes to ±∞ vertically, extend the interval to −∞ or ∞.
- Include y-values of isolated points (their y coordinate).
- Write the union of y-intervals/points.
Example notation:
- If a function exists for all x ≥ −2 and x ≤ 3 but not in between, write domain = (−∞, −2] ∪ [3, ∞) (example only).
- If the function attains all y between −1 and 4 including endpoints, write range = [−1, 4].
If you re-upload the graph or give a brief description (e.g., “line from x = −3 to 1 with solid at −3 open at 1; a filled dot at (2,0); and an arrow continuing to the right from (1,2)”), I’ll give the exact domain and range.
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