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Determining bounds of a function

  1. Sep 26, 2010 #1
    1. The problem statement, all variables and given/known data

    decide if f is bounded above or below, and if f takes on maximum or minimum value
    f(x)= x^2 for x< or =a, a+2 for x>a
    on (-a-1, a+1), assuming a>-1

    2. Relevant equations

    x^2 is continuous on R

    3. The attempt at a solution

    I have no idea where to start with this. I can constrain a+2 to (-1, a+1), but I don't know how that applies to the bounds of the entire function.
  2. jcsd
  3. Sep 27, 2010 #2


    Staff: Mentor

    Start by sketching a graph of this function. a is not given, so just pick some point on the positive x-axis and label it a. You might need to do this for several values of a, including at least one negative value.

    Alternatively, you could choose a few specific values of a and graph this function for each of them, and see how the graphs are similar.

    That's how I would start.
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