Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Asymptotes
Intercepts
Formulas
f(x) = (ax^2 + 12) / (x^2 + b)
Vertical Asymptote: x = sqrt(-b) when the denominator is zero
Y-Intercept: f(0) = 12 / b
Theorems
Behavior of rational functions near vertical asymptotes
Intercept calculation for rational functions
Suitable Grade Level
Grades 9-12
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