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# Question

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How do you figure out if an absolute value function like |y|=|x| is symmetric to the x-axis, y-axis, or the origin?

Aug 21, 2017

#1
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How do you figure out if an absolute value function like |y|=|x| is symmetric to the x-axis, y-axis, or the origin?

There is 2 posibilities

either y=x   or y=-x

so

$$|y|=|x|\\ \text{is equivalent to}\\ y=x\;\;\;\cup\;\;\;y=-x$$

To me it is obvious that this is symmetrical about both the x and the y axis

And it has point symmetry of degree 4 about (0,0)

Maybe to you it is not obvious..

You could draw it and see

OR

If it is symmetrical about the y axis then  for any point x=a and x=-a, the y value/s will be the same.

That is true, both times the y value can be a or -a

If it is symmetrical about the y axis then  for any point y=b and y=-b, the x value/s will be the same.

That is true, both times the x value can be b or -b

SO it is symmetrical about both the x and the y axes.

Here is the graph :) Aug 22, 2017
#2
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Thank you Melody. Aug 22, 2017