Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.
-x4 + y4 = 10
A)x-axis only
B)Origin only
C)x-axis, y-axis, origin
D)y-axis only

Question

Quizplus · Accepted Answer

The equation is symmetric with respect to the x-axis, y-axis, and the origin. For the x-axis, replacing $y$ with $-y$ gives the same equation $(x^4 + (-y)^4 = 10)$, indicating symmetry. For the y-axis, replacing $x$ with $-x$ also gives the same equation $((-x)^4 + y^4 = 10)$, indicating symmetry. For the origin, replacing both $x$ with $-x$ and $y$ with $-y$ gives the same equation, indicating symmetry.

Determine Algebraically Whether the Graph Is Symmetric with Respect to the X-Axis