It's symmetrical with respect to the x-axis
because if we replace x by -x and simplify, we
get the same equation we started with:
It's symmetrical with respect to the y-axis also
because if we replace y by -y and simplify, we
get the same equation we started with:
It's symmetrical with respect to the origin
because if we replace x by -x and y by -y
at the same time and simplify, we also
get the same equation we started with:
Next we find some first quadrant points.
Choose
Substitute in
This gives and
So a point in the first quadrant is (0,1)
(Actually it's a point on the BORDER of the first
quadrant, on the y-axis)
Choose
Substitute in
This gives and
So a point in the first quadrant is (0,),
which is about (1, .9)
Choose
Substitute in
This gives
So another point in the first quadrant is (2,0)
(Actually it's another point on the BORDER of the first
quadrant, this time on the x-axis)
Plot those three first quadrant points:
Next by the symmetry, we can reflect these three points
in both the x-axis and the y-axis, (like a mirror!) and
we have this:
Now we can sketch the curve:
Edwin