Function symmetry: -f(x), f(-x), -f(-x)

If f(x) == f(-x)    (≡ -f(x)=-f(-x))    then f is Y-axis symmetric, i.e. Even.

If f(-x) == -f(x)    (≡ f(x)=-f(-x))    then f is Origin symmetric, i.e. Odd.

f(x) f(-x) -f(x) -f(-x) symmetry?
1
x
x+1
x2+1
x2+x+1
x3
x3+1
x3-x
1/x
1/x2
|x|+1
ex
log x
sin x *
cos x *
tan x *
0 *

Look at the graph of each function f to confirm the symmetry or not.