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

Answer 1

Caleb Alexander

#2x^2##>=#0 thus y=f(x)#>=#0

f(-x)=2*#(-x)^2#=#2x^2#=f(x)

thus the graph is symmetric with respect to the y axis

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Answer 2

Serenity Jones

To determine the symmetry of the graph of (|y| = 2x^2):

Substitute (y = |y|) and (y = -|y|) into the equation separately.
Simplify each equation.
Check whether the resulting equations are equivalent when replacing (x) with (-x) for symmetry with respect to the y-axis, or when replacing (y) with (-y) for symmetry with respect to the x-axis.

If replacing (x) with (-x) (for y-axis symmetry) or (y) with (-y) (for x-axis symmetry) doesn't produce equivalent equations, then the graph is neither symmetric with respect to the x-axis nor the y-axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.