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Math Help - FUNCTIONS??? No clue how to do these.

  1. #1
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    FUNCTIONS??? No clue how to do these.

    ok, one of the "easier" ones...

    what is the range of the function, f(x )= 2x - 7x + 1 , -2 ≤ x ≤ 3

    thanks in advance to anyone who can help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by juliak View Post
    ok, one of the "easier" ones...

    what is the range of the function, f(x )= 2x - 7x + 1 , -2 ≤ x ≤ 3

    thanks in advance to anyone who can help
    remember, the range is the set of y-values for which your function is defined, given some domain. on an unrestricted domain, a parabola where the coefficient is positive has range [ \text{vertex}, \infty). so start there, but note that you can't go all the way up to \infty here, since your domain is restricted
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  3. #3
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    ok yeah i see that, but where do i start to figure it out?
    i get that the second part restricts it, but where do i go from there?
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  4. #4
    Senior Member vincisonfire's Avatar
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    You want the maxima and minima of the function.
    Find the local extrema and see if it is between -2 and 3 and evaluate f(-2) and f(3). The minimal value is your minima, same for maxima and these are the boundaries of the range.
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by vincisonfire View Post
    You want the maxima and minima of the function.
    Find the local extrema and see if it is between -2 and 3 and evaluate f(-2) and f(3). The minimal value is your minima, same for maxima and these are the boundaries of the range.
    As Jhevon pointed out, the minimum value (y-coordinate of vertex) is the lower boundary of the range. The upper boundary will be f(-2) or f(3), whichever yields the largest value for y.
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