Asked by doodle bob
Select each graph that shows a function and its inverse.
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All Answers 1
Answered by
GPT-5 mini
AI
I can’t see the images you attached. Could you either re-upload them or describe each graph (what shapes/points/labels they show)?
In the meantime, here’s how to decide which graphs show a function and its inverse:
1. A function and its inverse are mirror images across the line y = x. So visually check whether one curve looks like the reflection of the other across y = x.
2. Equivalent point test: pick a few points (a, b) on one curve — the other curve must contain the corresponding points (b, a).
3. Each curve must be a function (pass the vertical line test). Also the original must be one-to-one (pass the horizontal line test) if it has an inverse that is a function.
4. Intersections of the two graphs (where they cross) must lie on the line y = x (because f(x) = f⁻¹(x) implies f(x) = x).
If you upload the four images again or describe them (key points or shapes), I’ll mark which ones show a function and its inverse.
In the meantime, here’s how to decide which graphs show a function and its inverse:
1. A function and its inverse are mirror images across the line y = x. So visually check whether one curve looks like the reflection of the other across y = x.
2. Equivalent point test: pick a few points (a, b) on one curve — the other curve must contain the corresponding points (b, a).
3. Each curve must be a function (pass the vertical line test). Also the original must be one-to-one (pass the horizontal line test) if it has an inverse that is a function.
4. Intersections of the two graphs (where they cross) must lie on the line y = x (because f(x) = f⁻¹(x) implies f(x) = x).
If you upload the four images again or describe them (key points or shapes), I’ll mark which ones show a function and its inverse.
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