Question

how to know if the function is even or odd?

Answer 1

if the variable's leading power is even then it's even & if the variable's leading power is odd then it's odd? am I right?

Answer 2

No there is only one criteria to check if a function is even or odd and that is to use its definition
for instance
odd:\[f(-x)=f(x)\]try \[f(x)=x^2\implies f(-x)=(-x)^2=x^2=f(x)\huge\checkmark\]

Answer 3

arytttttttt

Answer 4

this also works with \[f(x)=\cos x\] because \[\cos(-x)=\cos x\] by the properties of trigonometry

Answer 5

oh those are all even above
I had it backwards, sorry :P

Answer 6

even\[f(-x)=f(x)\]odd:\[f(-x)=-f(x)\]for instance...

Answer 7

is \[f(x)=x^3+\frac x{|x|}+\sin x\]even, odd, or neither?