Finding intercepts and symmetry, but y is in both sides.

Ilovenayoon

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Sep 29, 2012
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The equation is
y=x4/(x+y)

What i have to do is,
(1) find x- and y-intercepts
(2) find any symmetry (y- or x-axis, origin, y=x)
(3) sketch a graph.


Since y is in both side, i cant think of the way.
Please help!!
 
The equation is
y=x4/(x+y)

What i have to do is,
(1) find x- and y-intercepts
(2) find any symmetry (y- or x-axis, origin, y=x)
(3) sketch a graph.

Since y is in both side, i cant think of the way.

1) To find the intercepts, follow the usual procedure: Plug zero in for x and solve for the y-intercept(s); plug zero in for y and solve for the x-intercept(s).

2) What rules do they give you for "finding symmetry"?

3) You might find it helpful to apply the Quadratic Formula to this:

. . . . .\(\displaystyle \displaystyle y\, =\, \frac{x^4}{x\, +\, y}\)

. . . . .\(\displaystyle \displaystyle y(x\, +\, y)\, =\, x^4\)

. . . . .\(\displaystyle \displaystyle y^2\, +\, xy\, -\, x^4\, =\, 0\)

. . . . .\(\displaystyle \displaystyle y\, =\, \frac{-x\, \pm\, \sqrt{x^2\, +\, 4x^4\,}}{2}\)

...and so forth.
 
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