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Question 43101: Please help with this:
Is the following symmetric with respect to the x axis, y axis, origin, or no symmetry?
y= (1)/(x^2 + 1)
to clear up my writing, x^2 is the same as x squared.
thanks
Found 2 solutions by ilana, stanbon:
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! You can just test values. If it is symmetric wrt (with respect to) the x-axis, then a value of y will give you the same x as -y. If it is symmetric wrt the y-axis, a value for x will give you the same y as -x. And if it is symmetric wrt the origin, then (x,y) will become (-x,-y).
So, let's test each. If we plug in any x and any -x, the corresponmding y will be the same because x only appears once in this equation, and it is x^2. So this is symmetric wrt the y-axis. If we try to do the same for y, we see that a negative value for y will have no corresponding x (since 1/(x^2 + 1) is always positive). So this is not symmetric wrt the x-axis. And finally, since it never goes below the x-axis, it cannot be symmetric wrt the origin. So it symmetric only wrt the y-axis.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Is the following symmetric with respect to the x axis, y axis, origin, or no symmetry?
y= (1)/(x^2 + 1)
f(x)= 1/(x^2+1)
f(-x)=1/((-x)^2+1) = 1/x^2+1
-f(-x)= -1/((-x)^2+1)= -1/(x^2+1)
Since f(x) = f(-x) you have y-axis symmetry.
Since f(x) is not equal to -f(-x) you do not have origin symmetry.
Since y does not equal -y you do not have x-axis symmetry.
Cheers,
stan H.
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