Math Problem Statement
y = 5 / [(3x + 1)(7x - 2)]
Solution
The given equation from the image is:
This is a rational function where is expressed as the quotient of a constant 5 and the product of two linear expressions, and .
Key Aspects:
- Numerator: is a constant.
- Denominator: The denominator is the product of two factors, and , both of which are linear terms in .
To explore the properties of this function further:
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Domain: The domain excludes values of where the denominator equals zero. We solve: This gives: Solving for : So, the domain of is all real numbers except and .
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Vertical Asymptotes:
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Domain and Asymptotes
Formulas
y = 5 / [(3x + 1)(7x - 2)]
Theorems
Vertical Asymptotes
Domain Restrictions
Suitable Grade Level
Grades 9-12