How do you determine whether the graph of $y^{2} = x^{2}$ $y^2=x^2$ is symmetric with respect to the x axis, y axis or neither?

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How do you determine whether the graph of $y^{2} = x^{2}$ $y^2=x^2$ is symmetric with respect to the x axis, y axis or neither?

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Answer 1 · 2017-01-24T16:29:26

Symmetrical about both x and y axes.

Explanation:

For symmetry about the y axis, see if $y (x) = y (- x)$ $y(x) = y(-x)$

Here you have:

$y = \pm \sqrt{x^{2}} = \pm | x |$ $y = pm sqrt(x^2) = pm abs x$ .

So $y (- x) = \pm | - x | = \pm | x |$ $y(-x) = pm abs (-x) = pm abs x$ . Looks symmetrical about the y axis.

Likewise, for symmetry about the x axis, see if $x (y) = x (- y)$ $x(y) = x(-y)$ .

In this case:

$x = \pm \sqrt{y^{2}} = \pm | y |$ $x = pm sqrt(y^2) = pm abs y$ . So $x (- y) = \pm | - y | = \pm | y |$ $x(-y) = pm abs (-y) = pm abs y$ . Looks symmetrical about the x axis.

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How do you determine whether the graph of $y^{2} = x^{2}$ $y^2=x^2$ is symmetric with respect to the x axis, y axis or neither?

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Explanation:

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How do you determine whether the graph of $y^{2} = x^{2}$ $y^2=x^2$ is symmetric with respect to the x axis, y axis or neither?