Question

Discuss the symmetry of the graph of the polynomial function.
f(x)=x^5-x

Answer 1

This is an odd function. How?
f(x) = x^5 - x
f(-x) = (-x)^5 - (-x) = -x^5 + x = -(x^5 - x) = -f(x)
So whenever f(-x) = -f(x) it is an odd function.
Odd functions are symmetric about the origin.

Answer 2

I see-thx

Answer 3

You are welcome.

FYI: Even function is when f(-x) = f(x). Example f(x) = x^2.
Even functions are symmetric about the y-axis.

Answer 4

Very helpful, thx