how do u determine if a function is even or odd?

Question

anonymous · Answer

several ways. 
1) if it is polynomial, all powers must be even (odd)
2) if you have a graph is must be symmetric wrt the y - axis (origin)
3) work from the definitions  

f is even if 
$$f(x)=f(-x)$$  odd if 
$$f(-x)=-f(x)$$

anonymous · Answer

can u plz do an example of f(-x)

anonymous · Answer

even:
 
$$f(x)=x^4-3x^2+1$$
$$g(x)=|x|$$

anonymous · Answer

sure lets take 
$$f(x)=\frac{x}{x^2+1}$$

anonymous · Answer

then 
$$f(-x)=\frac{-x}{(-x)^2+1}=\frac{-x}{x^2+1}=-\frac{x}{x^2+1}=-f(x)$$

anonymous · Answer

so that one is odd

anonymous · Answer

o ok i get it thx!

anonymous · Answer

yw

anonymous · Answer

u just put the (-) for any x

anonymous · Answer

you replace x by -x and see what you get.  most function are neither even nor odd

anonymous · Answer

k thx

anonymous · Answer

$$f(x)=x^2+2x+1$$
$$f(-x)=(-x)^2+2(-x)+1=x^2-2x+1$$ and this is not the same as what you started with or its negative, so it is neither

anonymous · Answer

o.. ok we learned this in class and i forgot what to do but now i remeber. Thx!