Asked by james
Given mc001-1.jpg, what is the domain?
mc001-2.jpg
mc001-3.jpg
mc001-4.jpg
all real numbers
What is the range?
mc002-1.jpg
mc002-2.jpg
mc002-3.jpg
all real numbers
All Answers 1
Answered by
GPT-5 mini
AI
I can’t open image filenames — please either upload the actual images or describe the graph(s). Without seeing the picture I can’t be sure whether the domain or range is “all real numbers.”
If you want to check yourself, here are quick rules to determine domain and range from a graph:
How to find the domain (x-values allowed)
- Look left-to-right: if the graph has arrows pointing left and right with no breaks, domain is all real numbers (−∞, ∞).
- If there is a vertical asymptote or a hole at x = a, exclude that x-value (or those x-values).
- If the graph stops at an endpoint, include that x if the endpoint is a filled dot, exclude if it’s an open dot.
- For functions defined by formulas: exclude x where denominators = 0 or where you take even roots of negative numbers or where logs have nonpositive arguments.
How to find the range (y-values attained)
- Look bottom-to-top: if the graph extends up and down without bound, range is all real numbers.
- If the graph has a highest or lowest point, include it if that point is a filled dot, exclude it if open.
- Vertical asymptotes, holes, and horizontal bounds remove or restrict y-values similarly.
- For formulas you can sometimes solve for x in terms of y and see which y give real solutions.
If you upload the images or describe: e.g. “graph is a parabola with vertex at (2,−3) opening up” or “graph is y = 1/(x−1) with vertical asymptote x=1”, I’ll give the exact domain and range.
If you want to check yourself, here are quick rules to determine domain and range from a graph:
How to find the domain (x-values allowed)
- Look left-to-right: if the graph has arrows pointing left and right with no breaks, domain is all real numbers (−∞, ∞).
- If there is a vertical asymptote or a hole at x = a, exclude that x-value (or those x-values).
- If the graph stops at an endpoint, include that x if the endpoint is a filled dot, exclude if it’s an open dot.
- For functions defined by formulas: exclude x where denominators = 0 or where you take even roots of negative numbers or where logs have nonpositive arguments.
How to find the range (y-values attained)
- Look bottom-to-top: if the graph extends up and down without bound, range is all real numbers.
- If the graph has a highest or lowest point, include it if that point is a filled dot, exclude it if open.
- Vertical asymptotes, holes, and horizontal bounds remove or restrict y-values similarly.
- For formulas you can sometimes solve for x in terms of y and see which y give real solutions.
If you upload the images or describe: e.g. “graph is a parabola with vertex at (2,−3) opening up” or “graph is y = 1/(x−1) with vertical asymptote x=1”, I’ll give the exact domain and range.
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