# SOLUTION: 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

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: 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       Log On

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 Click here to see ALL problems on Linear-equations 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(57352)   (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.