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Math Help - continuous function

  1. #1
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    continuous function

    I keep getting confused on this problem. So it is:

    determine a and b so that the following function is continuous on (-infinity, infinity)

    f(x)= 3x-2, x is less than or equal to 4 and greater or equal to 2.

    f(x)= x^2+ax+b, absolute value of (x-3) is greater or equal to 1.
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  2. #2
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    1) I'm pretty sure you have that first one a little backwards. Perhaps x <= 2 or x >= 4?

    2) It will help to separate the definition, so I'll use

    f(x) = 3x-2
    g(x) = x^2 + ax + b

    We'll just use g(x) when we are around x = 3 and g(x) when one (1) or more away.

    Your task is to create a continuous function. The only trick is matching up the endpoints, since (thankfully) they are the same).

    f(2) = 4
    f(4) = 10

    We must make g(2) = 4 and g(4) = 10

    That's all. Let's see what you get.
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  3. #3
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    got it!

    ok i got it.

    so

    4+2a+b=4
    2a+b=0

    and

    16+4a+b=10
    4a+b=-6

    a=-3
    b=6

    so if the x wasn't the same for both functions, then we couldn't solve this?
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  4. #4
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    If the Domains don't match up rationally.

    For example,

    Find 'b' that makes this continuous.

    f(x) = 3x - 5 for x < -10

    g(x) = -3x + b for x > 4

    It's silly. There's a giant gap!
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  5. #5
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    oh i see.

    do you tutor at a school or do private tutoring/know anyone in hawaii that helps calculus students??
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