The function f(x) = x / (x2 - 4) has asymptotes at?

The function f(x) = x / (x2 - 4) has asymptotes at?

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  • 1 decade ago
    Favorite Answer

    at x = +/- 2

    f(x) = x / (x^2 - 4)

    = x / (x-2)(x+2)

    because the denominator is the difference of two squares

    Asymptotes occur particularly when the denominator = 0 and therefore x = 2 or -2

    Alternatively

    x^2 - 4 = 0 using your original denominator

    x^2 = 4

    x = +/- 2

    and y does not = 0 at the asymptote ... oh - I see what they mean. Horizontal asymptote at 0 as x tends towards infinity

  • 1 decade ago

    Asymptotes are parts of the graph where the function is undefined because of division by zero, so set the denominator = 0 and solve

    x^2 - 4 = 0

    x^2 = 4

    x = +/- 2

  • 1 decade ago

    if I assume that it is x^2 then the answer is +2 and - 2. these two numbers will make 0 in the denominator which would be the asymptote.

    If you meant 2x, then the answer is just 2.

  • TFV
    Lv 5
    1 decade ago

    1) x = 2 or -2 [makes the denominator zero]

    2) y = 0 [f(x) approaches 0 as x approaches + or - infinity]

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  • talr
    Lv 4
    1 decade ago

    x = 2

    x = -2

    y = 0

    (All that assuming "x2" means x squared)

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