Question

consider the following equation:
\\f(x) = \frac{x^2 + 4}{4x^2 - 4x - 8}\\

name the vertical asymptote(s).

Explanation:

Identify the rational function

Using the Rational Functions knowledge point

$$ f(x) = \frac{x^2 + 4}{4x^2 - 4x - 8} $$

Factor the denominator

Using the Polynomial Factoring knowledge point

$$ 4x^2 - 4x - 8 = 4(x^2 - x - 2) = 4(x - 2)(x + 1) $$

Determine the vertical asymptotes

Using the Vertical Asymptotes knowledge point

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Answer:

Consider the following equation: \(f(x) = \frac{x^2+4}{4x^2-4x-8}\)

Name the vertical asymptote(s). <blank>\(x = 2, x = -1\)</blank>