Results 1 to 3 of 3

Math Help - Simple Question About "Graphs of Logarithmic Function"

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    1

    Question Simple Question About "Graphs of Logarithmic Function"

    First of all, glad to be one of your members.

    Simple Question About "Graphs of Logarithmic Function"-untitled.jpg

    Can you please explain to me the first row and the second one! I didn't get it yet.

    This is the graph:

    Simple Question About "Graphs of Logarithmic Function"-untitled2.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Dec 2005
    Posts
    34
    domain means what x values are rellevant for this function

    range means what y values are possible as a result of the function

    have a good day
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,596
    Thanks
    1421
    In this case the domain of f(x)= e^x is all real numbers because we can calculate 2^{x} for x any real number. And, of course, the result of that calculation is always a positive number and can be any positive real number. That is why the range is all positive real numbers.

    For f(x)= log_2(x), the domain is all positive numbers because log_2(x) (or logarithm of any base) is defined for all positive numbers but not for 0 or any negative numbers. If 0< x< 1, though, log_2(x)< 0 and log_2(1)= 0 so the range is all real numbers.

    In fact, for any positive number, a, a^x and log_a(x) are inverse functions: if y= a^x then x= log_a(y) so they "swap" domain and range. That is also why the graphs are symmetric about the line y= x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Very simple question on "definite integrals"
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 17th 2011, 05:48 AM
  2. Replies: 3
    Last Post: October 28th 2010, 10:40 PM
  3. "simple" math question
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 4th 2010, 12:09 PM
  4. "simple" polynomial question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: August 21st 2009, 05:50 AM
  5. Replies: 3
    Last Post: October 30th 2008, 03:19 PM

Search Tags


/mathhelpforum @mathhelpforum