Come si determina se #f (x) = (x) ^ 2 -x # è una funzione pari o dispari?

To determine if f(x) is even/odd consider the following.

• If f(x) = f( -x) , then f(x) is even

Even functions have symmetry about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd

Odd functions have symmetry about the origin.

Test for even

#f(-x)=(-x)^2-(-x)=x^2+x≠f(x)#

Since f(x) ≠ f( -x) , then f(x) is not even.

Test for odd

#-f(x)=-(x^2-x)=-x^2+x≠f(-x)#

Since f( -x) ≠ - f(x) , then f(x) is not odd.

Thus f(x) is neither odd nor even.
graph{x^2-x [-20, 20, -10, 10]}