Is the function #f(x) = x^3# symmetric with respect to the yaxis?
1 Answer
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.