Results 1 to 5 of 5

Math Help - Checking for symmetry

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    98

    Checking for symmetry

    Reading on how to check for symmetry, book uses this equation y=x^3. I am asked to do the same but with this equation;
    y=-5x

    I want to know if I did right or done something wrong...

    In looking for points to plot I did the following:

    X___Y
    0___0
    1___-5
    2___-10
    -1___5
    -2___10


    Now, about checking these points for symmetry. If I was to check for the y Axis I would have to replace x by -x, so then the equation would look like this;

    y=-5-x correct?

    So my Y axis ends up being positive y=-5(-1) = y=5 right?

    And if checking for the x Axis I would replace y by -y, -y=-5x

    so now my y axis remains a negative thus giving me this;

    -y=-5(1) = y=-5 so far correct?




    So for this equation y=-5x, we can say that it is only symmetric with respect to the origin, yes?!

    Thanks for taking the time on this!


    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    You seem to have the right idea, but a few values never will be sufficient. You must prove generally that f(x) = -f(-x).

    f(x) = x^{3}

    -f(-x) = -(-x)^{3} = x^{3} = f(x)
    Last edited by TKHunny; February 7th 2008 at 04:53 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    Posts
    98
    Quote Originally Posted by TKHunny View Post
    You seem to have the right idea, abut a few values never will be sufficient. You must prove generally that f(x) = -f(-x).

    f(x) = x^{3}

    -f(-x) = -(-x)^{3} = x^{3} = f(x)
    ... sorry, when you say "will never be sufficient", you mean once graphed? And how does f(x) work into y=-5x?

    many thanks again!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Morzilla View Post
    Reading on how to check for symmetry, book uses this equation y=x^3. I am asked to do the same but with this equation;
    y=-5x

    I want to know if I did right or done something wrong...

    ...
    There are two different types of symmetries which could be checked very easily. (There are others which are a lot more difficult to handle):

    1. Symmetry about the y-axis.

    If the graph of a function is symmetric about the y-axis all x-values from the domain of the function has to satisfy the equation:

    f(x) = f(-x)

    With your example:

    -5x\  {\buildrel \rm ? \over =}\  -5(-x)~\implies~-5x \ne 5x . So you know that the graph of this function is not symmetric to the y-axis.

    2. Symmetrie about the origin.

    If the graph of a function is symmetric about the origin all x-values from the domain of the function has to satisfy the equation:

    f(x) = -f(-x)

    With your example:

    -5x\  {\buildrel \rm ? \over =}\ -\left( -5(-x)\right)~\implies~-5x = -5x . So you know that the graph of this function is symmetric to the origin.


    Yes, you are right!
    Last edited by earboth; February 3rd 2008 at 10:16 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Quote Originally Posted by Morzilla View Post
    "never will be sufficient"
    I mean always. DISproof requires only one counter example. It is of no consequence if you can show 6,423,010 examples. To prove that something is ALWAYS the case, you cannot do it unless you can demonstrate it for EVERY case. That is a tall order for all Real Numbers unless you can establish a continuous relationship.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Symmetry
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 2nd 2009, 03:57 PM
  2. Symmetry
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 17th 2009, 10:16 PM
  3. Symmetry
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 23rd 2009, 06:54 PM
  4. Symmetry
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 11th 2007, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum