Given the function: $ f(x) = \frac{7x^2 - 2x + 3}{14x^2 + 5x - 8} $ Identify the horizontal asymptote. a....

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12. Given the function: $ f(x) = \frac{7x^2 - 2x + 3}{14x^2 + 5x - 8} $ Identify the horizontal asymptote. a. $ y = 7 $ b. $ y = \frac{1}{2} $ c. $ y = \frac{14}{7} $ d. $ y = -\frac{2}{5} $

SnapAndSolve AI · Accepted Answer

The horizontal asymptote of a rational function is determined by the degrees of the polynomials in the numerator and the denominator: If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = (leading coefficient of the numerator)/(leading coefficient of the denominator). If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. In this case, the degrees of the numerator and the denominator are both 2. Therefore, the horizontal asymptote is:y = $ \frac{7}{14} = \frac{1}{2} $The correct answer is b. $ y = \frac{1}{2} $

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Given the function: \( f(x) = \frac{7x^2 - 2x + 3}{14x^2 + 5x - 8} \) Identify the horizontal asymptote. a....

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