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Consider the following equation: f(x)=x²+4\4x²-4x-8 name the vertical asymptote(s)

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Final answer:

The vertical asymptotes of the given function f(x)=x²+4/4x²-4x-8 are x=1 and x=-1.

Step-by-step explanation:

The vertical asymptotes of a function represent values of x where the function approaches infinity or negative infinity. To find the vertical asymptotes of the given function f(x) = x²+4/4x²-4x-8, we need to determine the values of x that make the denominator equal to zero. So, we set 4x²-4x-8 = 0 and solve for x.

Factoring the quadratic equation gives us (2x-4)(2x+2) = 0. Solving the two factors separately, we find that x = 2/2 and x = -2/2. Simplifying, we get x = 1 and x = -1 as the values that make the denominator zero.

Therefore, the vertical asymptotes of the given function are x = 1 and x = -1.

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