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-   -   How do you determine the intervals in a function? (https://www.askmehelpdesk.com/showthread.php?t=373479)

  • Jul 8, 2009, 07:34 PM
    cowboys93
    How do you determine the intervals in a function?
    The question says,Graph the function and determine the intervals for which f(x) is greater than or equal to than 0.

    f(x)=4x+2

    Help pllleaseee
  • Jul 8, 2009, 08:21 PM
    Perito

    You wrote f(x) = 4x +2. What values of this are equal to zero? How about

    0 = 4x + 2?

    If you solve this for x, you'll see what value of x is zero. You can then figure out what values of x make the function greater than zero.

    Let me give you an example. Let's say that you have the equation

    f(x) = 17x - 34

    We look at the equation

    0 = 17x -34
    17x = 34
    x = 2

    So we know that f(x) = 0 for x = 2. What about x > 2? Let's try x=3

    f(3) = 17 * 3 - 34 = 17 yup > 0

    You can show that for any x > 2, f(x) will be greater than 0.

    What about x < 2?

    f(1) = 17 * 1 -34 = -17

    You can also show that for any x<2, f(x) will be less than zero.

    Therefore, for this equation, the intervals for which f(x) >= 0 are x= 2 to x= infinity

    You can also solve this equation

    17x - 34 >= 0

    17x >= 34

    x >= 2

    We haven't divided by any negative numbers, which would reverse the sign. We've just proven what we saw, above. You do the same thing for your equation:

    f(x) = 4x+2 >= 0

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