Math Problem Statement
Solution
To solve this problem, we need to understand the function given: . This function is defined only for because the square root of a negative number is not defined in the real number system.
For each of the given points , we will check if the -value matches .
Step-by-step evaluation:
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means we find the square root of and take its negative.
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We'll evaluate the function for the provided options:
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Option A:
- is not defined in the reals.
- is not defined in the reals.
- is not defined in the reals.
- None of these points are valid.
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Option B:
- For : , not .
- For : , not .
- For : , not .
- None of these points are valid.
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Option C:
- , , and are not defined in the reals.
- None of these points are valid.
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Option D:
- For : .
- For : .
- For : .
- All three points match.
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Conclusion:
Option D: contains points that lie on the graph of .
Would you like further details or have any questions?
Related Questions:
- How would the graph of differ from ?
- What is the domain and range of the function ?
- How do you find the square root of a negative number in complex numbers?
- What transformations are applied to the function to obtain ?
- How would you plot using a graphing calculator?
Tip:
Remember, for square root functions like or , the domain is restricted to non-negative values of .
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Math Problem Analysis
Mathematical Concepts
Square root function
Domain and range
Graphing functions
Formulas
f(x) = -√x
Theorems
Properties of square roots
Function transformations
Suitable Grade Level
Grades 9-12