Is the function #f(x) = x^3# 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)" "# for all#x# in the domain of#f(x)color(white)(0/0)# -
An odd function is a function satisfying:
#f(-x) = -f(x)" "# for all#x# in the domain of#f(x)color(white)(0/0)#
Even functions are symmetric with respect to the
Odd functions have rotational symmetry of order
Given:
#f(x) = x^3#
Note that for any value of
#f(-x) = (-x)^3 = (-1)^3 x^3 = -x^3 = -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.