Domain of Rational Function

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

  1. nycmathguy

    nycmathguy

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    Section 2.6
    Question 6

    20210920_230557.jpg

    f(x) = 5x/(x + 2)

    The denominator is zero when x = -2.

    x + 2 = 0

    x = -2

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

    To discuss the behavior of f near any excluded values of x, it is best to evaluate a few values to the left and right of x = -2.

    x-values left of 0

    Let x = -4

    f(-4) = 5(-4)/(-4 + 2)

    f(-4) = -20/-2

    f(-4) = 10

    Let x = -3

    f(-3) = 5(-3)/(-3 + 2)

    f(-3) = 15

    x-values right of 0

    Let x = 2

    f(2) = 5(2)/(2 + 2)

    f(2) = 10/4

    f(2) = 2.5

    Let x = 1

    f(1) = 5(1)/(1 + 2)

    f(1) = 5/3

    f(1) = 1.66

    As x nears -2 from the left side, the graph shoots upward to positive infinity.

    As x nears -2 from the right side, the graph shoots download to negative infinity.

    Is my understanding correct here?

    P. S. Please, check out my thread from yesterday at 9:16pm: Find Zeros of Polynomial Function.
     
    Last edited: Sep 21, 2021
    nycmathguy, Sep 21, 2021
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  2. nycmathguy

    MathLover1

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    discuss the behavior of f near any excluded values of x=-2 only

    all you need is:

    Limit from the left
    [​IMG]

    Limit from the right

    [​IMG]


     
    MathLover1, Sep 21, 2021
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  3. nycmathguy

    nycmathguy

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    1. This is a precalculus question. Why bring calculus into play?

    2. What's wrong with my thread?
     
    nycmathguy, Sep 21, 2021
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  4. nycmathguy

    nycmathguy

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    As x nears -2 from the left side, the graph shoots upward to positive infinity.

    As x nears -2 from the right side, the graph shoots download to negative infinity.

    Is this not the same as your limit reply?
     
    nycmathguy, Sep 21, 2021
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  5. nycmathguy

    MathLover1

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    yes, it's same as my limit reply :) just wanted to show you shorter way to do it
     
    MathLover1, Sep 21, 2021
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  6. nycmathguy

    nycmathguy

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    Thanks.
     
    nycmathguy, Sep 21, 2021
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