Is the function f(x) = x^3f(x)=x3 symmetric with respect to the y-axis?
1 Answer
No, it has rotational symmetry of order
Explanation:
-
An even function is a function satisfying:
f(-x) = f(x)" "f(−x)=f(x) for allxx in the domain off(x)color(white)(0/0)f(x)00 -
An odd function is a function satisfying:
f(-x) = -f(x)" "f(−x)=−f(x) for allxx in the domain off(x)color(white)(0/0)f(x)00
Even functions are symmetric with respect to the
Odd functions have rotational symmetry of order
Given:
f(x) = x^3f(x)=x3
Note that for any value of
f(-x) = (-x)^3 = (-1)^3 x^3 = -x^3 = -f(x)f(−x)=(−x)3=(−1)3x3=−x3=−f(x)
So
It is not symmetric with respect to the
graph{x^3 [-5, 5, -10, 10]}
In fact any polynomial consisting of only terms of odd degree will be an odd function and any polynomial consisting of only terms of even degree will be an even function.
