SOLUTION: Can you please help me?* my question is: Determine whether the graph of y=|4x| is symmetric with respect to the x-axis, the y-axis, or the origin

Rule:

1. Replace y by -y only and simplify.  If the simplified form is
identical to the original, then the graph is symmetric with
respect to the x-axis.

2. Replace x by -x only and simplify.  If the simplified form is
identical to the original, then the graph is symmetric with
respect to the y-axis.

3. Replace x by -x and y by -y and simplify.  If the simplified form is
identical to the original, then the graph is symmetric with
respect to the origin.

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We replace y by -y only and simplify.  





This does not simplify to the original, so it is not
symmetric with respect to the x-axis.

2. Replace x by -x only and simplify.  





This simplified form is identical to the original, 
so the graph is symmetric with respect to the y-axis.

3. Replace x by -x and y by -y and simplify. 



Replace y by -y only and simplify.  









This does not simplify to the original, so it is not
symmetric with respect to the origin.

So it is only symmetric with respect to the y-axis.

Here is the graph, and you can see that the y-axis is
the axis of symmetry.



Edwin