Question
Which is the graph of y equals inverse sine x?
(1 point)
Responses
A curve increases from left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis through the origin to left-parenthesis 1 comma start fraction pi over 2 end fraction right-parenthesis.
Image with alt text: A curve increases from left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis through the origin to left-parenthesis 1 comma start fraction pi over 2 end fraction right-parenthesis.
A curve decreases from left-parenthesis negative 1 comma pi right- parenthesis through the origin to left-parenthesis 1 comma 0 right-parenthesis.
Image with alt text: A curve decreases from left-parenthesis negative 1 comma pi right- parenthesis through the origin to left-parenthesis 1 comma 0 right-parenthesis.
A curve increases from a horizontal asymptote at y equals negative start fraction pi over 2 end fraction through the origin to a horizontal asymptote of y equals start fraction pi over 2 end fraction.
Image with alt text: A curve increases from a horizontal asymptote at y equals negative start fraction pi over 2 end fraction through the origin to a horizontal asymptote of y equals start fraction pi over 2 end fraction.
A graph of an inverse trigonometric function is shown.One branch of the graph is decreasing from a horizontal asymptote at y equals 0 to left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis. The other branch is decreasing from left-parenthesis one comma start fraction pi over 2 end fraction right-parenthesis to a horizontal asymptote at y equals 0.
Image with alt text: A graph of an inverse trigonometric function is shown. One branch of the graph is decreasing from a horizontal asymptote at y equals 0 to left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis. The other branch is decreasing from left-parenthesis one comma start fraction pi over 2 end fraction right-parenthesis to a horizontal asymptote at y equals 0.
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(1 point)
Responses
A curve increases from left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis through the origin to left-parenthesis 1 comma start fraction pi over 2 end fraction right-parenthesis.
Image with alt text: A curve increases from left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis through the origin to left-parenthesis 1 comma start fraction pi over 2 end fraction right-parenthesis.
A curve decreases from left-parenthesis negative 1 comma pi right- parenthesis through the origin to left-parenthesis 1 comma 0 right-parenthesis.
Image with alt text: A curve decreases from left-parenthesis negative 1 comma pi right- parenthesis through the origin to left-parenthesis 1 comma 0 right-parenthesis.
A curve increases from a horizontal asymptote at y equals negative start fraction pi over 2 end fraction through the origin to a horizontal asymptote of y equals start fraction pi over 2 end fraction.
Image with alt text: A curve increases from a horizontal asymptote at y equals negative start fraction pi over 2 end fraction through the origin to a horizontal asymptote of y equals start fraction pi over 2 end fraction.
A graph of an inverse trigonometric function is shown.One branch of the graph is decreasing from a horizontal asymptote at y equals 0 to left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis. The other branch is decreasing from left-parenthesis one comma start fraction pi over 2 end fraction right-parenthesis to a horizontal asymptote at y equals 0.
Image with alt text: A graph of an inverse trigonometric function is shown. One branch of the graph is decreasing from a horizontal asymptote at y equals 0 to left-parenthesis negative 1 comma negative start fraction pi over 2 end fraction right-parenthesis. The other branch is decreasing from left-parenthesis one comma start fraction pi over 2 end fraction right-parenthesis to a horizontal asymptote at y equals 0.
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Answers
Answered by
GPT-4o mini
The graph of \( y = \arcsin(x) \) or \( y = \sin^{-1}(x) \) is characterized by the following features:
- The domain is \( [-1, 1] \) (it only takes input values between -1 and 1).
- The range is \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \).
- The graph will start at the point \( (-1, -\frac{\pi}{2}) \) and end at \( (1, \frac{\pi}{2}) \).
- The graph is increasing throughout its domain.
Based on your descriptions, the correct option is:
**A curve increases from (−1, −\(\frac{\pi}{2}\)) through the origin to (1, \(\frac{\pi}{2}\)).**
This matches the definition of the graph of the inverse sine function.
- The domain is \( [-1, 1] \) (it only takes input values between -1 and 1).
- The range is \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \).
- The graph will start at the point \( (-1, -\frac{\pi}{2}) \) and end at \( (1, \frac{\pi}{2}) \).
- The graph is increasing throughout its domain.
Based on your descriptions, the correct option is:
**A curve increases from (−1, −\(\frac{\pi}{2}\)) through the origin to (1, \(\frac{\pi}{2}\)).**
This matches the definition of the graph of the inverse sine function.
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