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

The given function $y = 4x^{20} - x^{10} - 3$ is symmetric with respect to the y-axis because replacing $x$ with $-x$ results in the same function: $y = 4(-x)^{20} - (-x)^{10} - 3 = 4x^{20} - x^{10} - 3$. This is because the exponents of $x$ are even, which means the function does not change when $x$ is replaced with $-x$. This does not indicate symmetry with respect to the x-axis or the origin, as those would require different conditions to be met.

Use Algebraic Tests to Check the Following for Symmetry with Respect