Math Problem Statement
What the correct answer
Solution
The image shows the function .
It appears you're looking to solve or analyze something about this function. Since it's an expression for a rational function, here are a few potential directions you could explore:
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Domain: The domain of is all real numbers except , because division by zero is undefined.
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Range: The range of this function includes all real numbers except zero. Since the numerator is a constant (2), the function will never output 0.
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Asymptotes:
- Vertical asymptote: At , the function has a vertical asymptote, as the function tends toward infinity as approaches 0.
- Horizontal asymptote: As approaches either positive or negative infinity, approaches 0.
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Graph behavior: The graph of is a hyperbola, with two distinct branches: one in the first quadrant for positive values and one in the third quadrant for negative values.
If you were seeking a specific solution or analysis, feel free to clarify. Would you like to explore one of these concepts further, or do you have another type of question about this function?
Here are five related questions:
- What are the intercepts of the function ?
- How does the function behave as and ?
- Can we find the inverse of the function ?
- What is the derivative of with respect to ?
- How can we determine the concavity of the graph for ?
Tip: For rational functions like this, identifying the vertical and horizontal asymptotes gives a good sense of how the function behaves for large and small values.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Asymptotes
Formulas
h(x) = 2/x
Theorems
Vertical Asymptote
Horizontal Asymptote
Suitable Grade Level
Grades 9-12