One way to do it is to draw the graph. That would be rather instructive.
Clearly it not symmetric about the y axis because x cannot be negative. The lest side of the equation is always positive or zer.
For x > 0, there are two possible y values for each x (+x^3 and -x^3) , and they are symmetric about the x axis.
How would you determine whether |y|= x^3 is symmetric with respect to the x-axis, y-axis, both, or neither.
In my book it said to plug in (a,b) and to get an equation to compare the other ones to. So I got |b|= a^3. Then I plugged in (a,-b) to test the x-axis and (-a,b) to test the y-axis. So I got |-b|= a^3 and |b|= -a^3. So then I though that it would be symmetrical with respect to the x-axis, but when I graphed it, it was symmetrical with respect to the y-axis.
3 answers
Why x can't be negative? Isn't it just y that can't be negative?
If x is negative , you'd have a negative number on the right and a positive number (an absolute value) on the left. That cannot happen.
Try graphing it and you will see.
Try graphing it and you will see.
4 answers