Domain of Rational Function...2

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 21, 2021.

  1. nycmathguy

    nycmathguy

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    Section 2.6
    Question 8


    20210920_230557.jpg



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

    Set x^2 - 4 to zero and solve for x.

    x^2 - 4 = 0

    x^2 = 4

    sqrt{x^2} = sqrt{4}

    x = -2, x = 2.

    Domain = ALL REAL NUMBERS except for x = -2 and x = 2.

    I say the two x-values are the vertical asymptotes.

    Discuss the behavior of f near the excluded values of x.

    Limit of f(x) as x tends to -2 from the right side is positive infinity.

    Limit of f(x) as x tends to 2 from the left side is negative infinity.

    20210921_015356.jpg

    You say?
     
    Last edited: Sep 21, 2021
    nycmathguy, Sep 21, 2021
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  2. nycmathguy

    MathLover1

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    way to go!
     
    MathLover1, Sep 21, 2021
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  3. nycmathguy

    nycmathguy

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    nycmathguy, Sep 21, 2021
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