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Calculus functions

  1. Mar 15, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the Domain and sketch the graph of the function if a grid is provided.

    1. p(t) = | 2t + 3 |

    2. Relevant equations

    3. The attempt at a solution

    Well basically in the book it said that it would end up looking something like this.... {2t + 3 for (2t + 3) > 0 (<----- that is suppost to be greater or equal to)

    and the other part was suppost to be { -(2t + 3) for (2t + 3) < 0

    to me this makes no sense of why this is suppost to end up this way. Also ignore the part that said if you're provided a grid. You don't have to solve it or anything like that, but just explain this to me. Thank you, Corkery.
  2. jcsd
  3. Mar 15, 2007 #2
    Since the absolute value does not allow for negatives, the function must be split into the piecewise function of the part where it is negative, and the part where it is positive.
  4. Mar 16, 2007 #3
    why is one of the equations greater than or equal to zero and another is less then zero. I just don't understand why you would do this. Is there a lamens term explanation, haha or is it already in lamens terms?
  5. Mar 16, 2007 #4

    Gib Z

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    Homework Helper

    Basically, let 2t+3 = u

    Absolute value signs mean, keep the u positive at all costs! RAWR!

    so, when u is negative, less than zero, to make it postive stick another negative sign in front right?!

    When u is positive, leave it as it is.

    So that splits it into 2 bits thatll keep it positive!

    -(2t+3) for < 0, 2t+3 for > 0 :D:D
  6. Mar 16, 2007 #5
    WOW! I actually understand that! thank you so much GIB Z and thank you Mindscrape. You guys rock!
  7. Mar 16, 2007 #6
    or you can "read" the function

    let f(x)=|x|

    basically, you are asked to figure out the graph for

    the factor of two means 2 times narrower, +3/2 means translation to the left for 3/2 units.

    just transform the V shape according to the recipe and you are done.
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