Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $y = 4 x ^ { 20 } - x ^ { 10 } - 3$
A)No symmetry.
B)Symmetric with respect to the y-axis.
C)Symmetric with respect to the origin.
D)Symmetric with respect to the x-axis.

Question

Quizplus · Accepted Answer

A function is symmetric with respect to the y-axis if $f(-x) = f(x)$. For $y = 4x^{20} - x^{10} - 3$, replacing $x$ with $-x$ yields $y = 4(-x)^{20} - (-x)^{10} - 3 = 4x^{20} - x^{10} - 3$, which is the same as the original function, indicating symmetry with respect to the y-axis.

Use Algebraic Tests to Check the Following for Symmetry with Respect