Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
-$$y = 7 x ^ { 5 } - 9 x ^ { 3 }$$
A) origin only
B) $x$-axis, $y$-axis, origin
C) none of these
D) $y$-axis only

Question

Quizplus · Accepted Answer

The given equation $y = 7x^5 - 9x^3$ is symmetric with respect to the origin because replacing $x$ with $-x$ results in $y = 7(-x)^5 - 9(-x)^3 = -7x^5 + 9x^3$, which is the original equation negated ($-y$). This satisfies the condition for origin symmetry, where $f(-x) = -f(x)$.

Determine Whether the Equation Has a Graph That Is Symmetric y=7x5−9x3y = 7 x ^ { 5 } - 9 x ^ { 3 }y=7x5−9x3

Determine Whether the Equation Has a Graph That Is Symmetric $y = 7 x ^ { 5 } - 9 x ^ { 3 }$