Calculus

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I'm asked to find the domain of fuction

(x+5)/(x-3)

saying that x is all reals except for x can not equal three is wrong correct? Because i can evalue function when x = 3 as follows

3 + 5 = 8

so saying that the function has range x is a reals except x can not equal three is wrong because it can???

  • Calculus -

    No, it's not wrong.

    When x=3, we have:

    (x + 5) / ( x - 3)

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

    = 8 / 0

    which is undefined, because of division by zero.

  • Calculus -

    no its 8

  • HELP -

    I'm sure i did it right

  • Calculus -

    What is 8 divided by zero?

  • Calculus -

    no...
    also all reals is wrong because
    i know you can never get a value greater than -5/3

  • Calculus -

    wait what am I doing wrong here

    (X+5)/(X - 3)

    (x+5)/x
    --------
    (x-3)/x

    (1+5/X)
    --------
    (1-3/x)

    i forgot were to go from here

  • Calculus -

    (x+5)/(x - 3)

    is just

    (x+5)
    -----
    (x-3)

  • Calculus -

    1 + 0
    -------------
    1 - 0

    I'm just getting 1????

  • Calculus -

    oh...
    I did it right

    graph it if you don't believe me

  • Calculus -

    so the range is...
    y is...
    arg confused

  • Calculus -

    ...every number except 1?

  • Calculus -

    So how come we can not say that x can not equal 3 because I'm getting 8 when x = 3 also how come we say range is all reals when its not because y will never equal 1

  • Calculus -

    To the person posting as "Help"

    The reply by Jim is correct, division by zero is undefined and causes a vertical asymptote in the corresponding graph for the given function.

    Changing it to the form
    (1+5/X)
    --------
    (1-3/x)
    serves no purpose, since when x = 3 you are still dividing by zero.

    Changing it to that form would be useful if we wanted to find the horizontal asymptote, by letting x become "very large". We can see that the above would approach 1 and the H.A. would be y = 1

    As stated by jim, the domain is the set of real numbers, except x cannot be 3 .

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