How do you determine whether the graph of #f(x)=1/(4x^7)# is symmetric with respect to the origin?

1 Answer
Dec 31, 2016

Answer:

Find #f(-x) = -f(x)#, so #f(x)# is an odd function, with rotational symmetry of order #2# about the origin.

Explanation:

We find:

#f(-x) = 1/(4(-x)^7) = (-1)^7*1/(4x^7) = -1/(4x^7) = -f(x)#

So #f(x)# is an odd function.

Its graph is rotationally symmetric about the origin, with order #2#:

graph{1/(4x^7) [-10, 10, -5, 5]}