Determine if the following function is even, odd, or neither.

f(x) = –9x^4 + 5x + 3

show me steps please.

Question

Determine if the following function is even, odd, or neither.

f(x) = –9x^4 + 5x + 3

show me steps please.

anonymous · Answer

you got an even power, namely 4, and an odd power, namely 1, so  neither

anonymous · Answer

your teacher want you to do this

$$f(-x)=-9(-x)^4+5(-x)+3=-9x^4-5x+3$$ and since 
$$f(-x)\neq f(x)$$ it is not even
also since $f(-x)\neq -f(x)$ it is not odd

anonymous · Answer

notice that $-f(x)=-(-9x^4+5x+3)=9x^4-5x-3$ which is not the same as $f(-x)=-9x^4-5x+3$

anonymous · Answer

what do you mean f(−x)≠f(x)

anonymous · Answer

$f(x)=-9x^4+5x+3$ right?  and we computed 
$f(-x)=-9x^4-5x+3$

anonymous · Answer

so  they are not equal because one has $5x$ and the other has $-5x$

anonymous · Answer

because they are not the same, that means $f$ is not even

anonymous · Answer

here is an example of an even function: 
$$g(x)=x^4+x^2+1$$ in this example $$g(-x)=(-x)^4+(-x)^2+1=x^4+x^2+1=g(x)$$ so that one is even

anonymous · Answer

oh I see and how do we know it's not odd