Math Problem Statement
Consider a rational function f that satisfies the following conditions. lim x→±∞ f(x) = 0, lim x→0 f(x) = −∞, f(7) = 0,
lim x→8− f(x) = ∞, lim x→8+ f(x) = −∞, Find the factors of the denominator of f corresponding to the vertical asymptotes. (Enter your answers as a comma-separated list. Enter at least one expression for each vertical asymptote.)
Correct: Your answer is correct. Excellent! Find the factors of the numerator of f corresponding to the x-intercepts. (Enter your answers as a comma-separated list. Enter at least one expression for each x-intercept.)
Correct: Your answer is correct.
Good work!
Which of the following must be true?
The degrees of the numerator and the denominator are equal.
The degree of the denominator is greater than the degree of the numerator.
The degree of the numerator is greater than the degree of the denominator.
Correct: Your answer is correct.
That's it!
Find an equation for f.
f(x) =
Incorrect: Your answer is incorrect.
Solution
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Math Problem Analysis
Mathematical Concepts
Rational Functions
Asymptotes
Limits
Formulas
f(x) = (x - 7) / [x(x - 8)]
Limit properties of rational functions
Theorems
Limits at infinity and asymptotes
Factorization of polynomials
Suitable Grade Level
Grades 11-12
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