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Exponential and Logarithmic functions

  1. Jan 18, 2005 #1
    How do I find
    1. Domain & Range
    2. Intervals of increase/decrease
    3. max./min values
    4. intercepts
    5. asymptotes
    6. concavity

    for Exponential and Logarithmic functions. Can someone explain how I do this in detail plzzz

    These are the types of questions I have (plz don't solve them just tell me how to do them:

    y= 2x - lnx

    y = x^2lnx

    y= in(x-1)^2

    y = e^x + 1

    y= x - lnx
  2. jcsd
  3. Jan 18, 2005 #2
    This is a rather lengthy question, so lets just work on pieces at a time, how about the first equation y = 2x - lnx.
    Here are some hints:
    - What values of x make this function not meaningful? ( we can exclude these from the domain)
    - what can tell us about how a function changes wrt the indepenent variable? (hint it starts with a "d" and ends with "erivative"

    That should at least get you going( or thinking in the right direction),,, please show work of any progress and we'll be happy to help you further :tongue2:
  4. Jan 18, 2005 #3
    - What values of x make this function not meaningful? ( we can exclude these from the domain)

    0 or anything below??
  5. Jan 18, 2005 #4
    yes... since the natural log is not defined for any value of x (< or =) to 0

    I think this probably would have better gone under homework :uhh:
    Last edited: Jan 18, 2005
  6. Jan 20, 2005 #5
    I'm confused... :confused: with all the explaining.

    You can just say stuff like set y' = 0 and stuff like that for all of them.

    And thanks for trying to help
  7. Jan 21, 2005 #6
    The domain is all the numbers for which you can compute a function on the x-axis. The range is a set of all the numbers that can be computed for the y-axis.

    if im not mistaken the intervals of increase and decrease are seen by just taking the derivative of the function and checking to see if the values are positive or negative.

    The asymptotes of the function are easiest found by the limits for which as x->infinity y=a given value which would inturn give you the vertical limit. For the horizontal limit its the limit for which as x->a number the function goes to infinity.

    Hope that helps and please clairify me if i've made any mistakes.
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