1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rational functions and link with direct substitution property

  1. Oct 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Hello,

    I know the direct substitution property in calculus. But, the definition of a rational function still confuses me.

    For example, are these rational functions:

    y=(x^2+2x+1)/(x+1)

    y=((x^2+2)^(1/2))/(x+1)

    The denominator of the first one could cancel. So, is there still a ratio? Is it a rational function?

    The second one has a root in the numerator. The exponents of are not integers. Is it still a rational function?

    Please help me. I do not understand the definition.
     
  2. jcsd
  3. Oct 19, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    Rational expression: ratio of two polynomials; since 1 is a polynomial of order zero, y=x+1 is also a rational expression, as is y=1/x ... as long as you exclude zeros in the denominator.

    A rational function is just a function which can be written as a rational expression. Your second example is not a rational expression, so y is not a rational function.
     
  4. Oct 19, 2013 #3
    Thank you for the fast reply.
    But, what do you mean by rational expression? I do not quite get it.


    What about if there was an absolute value in the function?

    EDIT: I understand why the second one is not a rational expression! Thank you. I still have a doubt about absolute values.
     
    Last edited: Oct 19, 2013
  5. Oct 19, 2013 #4

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    Rational expression: from ratio of expressions - in this case the individual expressions are always polynomials, so a rational expression is simply the ratio of two polynomials.

    Your text may extend this to include absolute value of a ratio of polynomials, but that is not what is usually meant. But you always need to look at (and understand, and remember) the definition which is provided.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rational functions and link with direct substitution property
  1. Rational Functions (Replies: 8)

  2. Substituting functions (Replies: 2)

  3. Rational function (Replies: 6)

Loading...