Question 141040
Can you please help me?* my question is: Determine whether the graph of {{{y=abs(4x)}}} is symmetric with respect to the x-axis, the y-axis, or the origin
<pre><font size = 4 color = "indigo"><b>
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.

---------------------

{{{y=abs(4x)}}}

We replace y by -y only and simplify.  

{{{-y=abs(4x)}}}

{{{y=-abs(4x)}}}

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.  

{{{y=abs(4(-x))}}}
{{{y=abs(-4x)}}}
{{{y=abs(4x)}}}

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. 

{{{y=abs(4x)}}}

Replace y by -y only and simplify.  

{{{-y=abs(4(-x))}}}

{{{-y=abs(-4x)}}}

{{{-y=abs(4x)}}}

{{{y=-abs(4x)}}}

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.

{{{graph(400,375,-10,10,-10,10,abs(4x))}}}

Edwin</pre>