Final answer:
The vertical asymptotes of the equation f(x) = (x² - 4) / (4x² - 4x - 8) occur where the denominator is zero, which are x = 2 and x = -1.
Step-by-step explanation:
To find the vertical asymptote(s) of the equation f(x) = (x² - 4) / (4x² - 4x - 8), we need to look for values of x that make the denominator equal to zero since vertical asymptotes occur at these values. First, factor the denominator: 4x² - 4x - 8 = 4(x² - x - 2) = 4(x - 2)(x + 1). Set each factor equal to zero: x - 2 = 0, x + 1 = 0. Solving these equations gives us the x-values that are potential asymptotes: x = 2, x = -1. Therefore, the vertical asymptotes of the given function are x = 2 and x = -1.