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Math Help - Symmetry

  1. #1
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    Symmetry

    Determine whether the graph of the function is symmtetric about the y-axis, the origin, or neither.

    y= x^2 - 2x - 1

    Is it simply just plugging in -x for the values of x and all that jazz? The other one was y=x^(1/5). I found out that f(-x) = -f(x) so it was an odd function and symmetric with the origin. What's going on in the x^2 example?>
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  2. #2
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    Quote Originally Posted by fezz349 View Post
    Determine whether the graph of the function is symmtetric about the y-axis, the origin, or neither.

    y= x^2 - 2x - 1

    Is it simply just plugging in -x for the values of x and all that jazz? The other one was y=x^(1/5). I found out that f(-x) = -f(x) so it was an odd function and symmetric with the origin. What's going on in the x^2 example?>
    yes ... given that you understand the jazz.

    f(x) = x^2 - 2x - 1

    f(-x) = (-x)^2 - 2(-x) - 1 = x^2 + 2x - 1

    does f(-x) = f(x) or -f(x) ?

    if no, then no symmetry.
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  3. #3
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    Ok thanks a lot man, I can see that it doesn't equal to f(x), but i'm just not understanding it with the -fx . in the equation x^2 - 2x - 1 i don't understand what's going on with the "x" in the 2x? the x in x^2 becomes -x^2 with no parentheses, what about the second one?
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  4. #4
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    Quote Originally Posted by fezz349 View Post
    Ok thanks a lot man, I can see that it doesn't equal to f(x), but i'm just not understanding it with the -fx . in the equation x^2 - 2x - 1 i don't understand what's going on with the "x" in the 2x? the x in x^2 becomes -x^2 with no parentheses, what about the second one?
    f(x) = x^2 - 2x - 1

    -f(x) = -(x^2 - 2x - 1)

    ... change the signs

    -f(x) = -x^2 + 2x + 1
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