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Pre Cal

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what does it mean when it says describe the end behavior of f and whats that for f(x)=(x^2+x+3)/(x-1)
and f(x)= 3*2^x,
please explain everything, and if you use --> tell me what that means, cuz i have no clue

  • Pre Cal - ,

    --> means "goes to"
    as in what happens to your function there as x goes to 1
    or as x --> 1

    As x -->1
    The numerator becomes 1+1+3 = 5
    so the function looks like 5/(x-1)
    but of course x-1 is 0 when x =1 so the function becomes undefined when x = 1
    but what if x = 1.001 for example
    then the function is about
    5/.001 or 5000
    and if x = .0001
    then it is about 50,000 very big
    Now look at x = .999
    then it is 5/-.001 = -5000
    and if x = .9999 then f = -50,000
    do we see a trend here?
    graph it.
    Now what happens as x-->oo
    when x is big, x^2 is much bigger than x or 3
    so the numerator looks like x^2
    similarly the denominator looks like x
    so for big +x the function looks like just plain old x, a straight line of slope +1
    And if you do x-->-oo
    then the numerator is positive x^2 and the denominator looks like x so the result is again looks like x, that same straight line of slope +1

  • Pre Cal - ,

    what is the big +x?
    and so the answer is
    "so for big +x the function looks like just plain old x, a straight line of slope +1" and "then the numerator is positive x^2 and the denominator looks like x so the result is again looks like x, that same straight line of slope +1"? if so is there an easier way to write that?

  • Pre Cal - ,

    what is the big +x?

    In other words what happens when x is a large positive number.

  • Pre Cal - ,

    ok, that's wahat i thought but wasn't sure.

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