How do you determine whether the graph of $y = \sqrt{2 - x^{2}}$ $y=sqrt(2-x^2)$ is symmetric with respect to the x, y axis?

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Answer 1 · 2016-11-28T15:16:39

See explanation

Square both sides giving

$y^{2} = 2 - x^{2}$ $y^2=2-x^2$

$x^{2} + y^{2} = 2$ $x^2+y^2=2$

This is the equation of a circle centred at the origin

Thus is symmetrical about both the x and y axis
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Note that the question does NOT use the format $y = \pm \sqrt{2 - x^{2}}$ $y=+-sqrt(2-x^2)$

How do you determine whether the graph of y=√2−x2y=sqrt(2-x^2) is symmetric with respect to the x, y axis?