Question

Are these functions odd, even, or neither?

1.f(x) = -x^6 + 3x^3 + 2x -7

(i think even)

2.f(x) = -x^4 + 2x^4
(i think neither)

Answer 1

f(x) = -x^6 + 3x^3 + 2x -7

notice how the exponents are both odd and even

this mix means the function is neither

Answer 2

if you want an odd function, all exponents must be odd
if you want an even function, all exponents must be even

Answer 3

this trick only works with polynomials

Answer 4

aah, okay, thank you! :)

Answer 5

you're welcome

Answer 6

also you can use the definition

\(EVEN \iff f(-x) = f(x)\)
\(ODD \iff f(-x) = -f(x)\)
\(NEITHER \iff NOT \ ODD \ AND \ NOT \ EVEN\)

Answer 7

wait, @jim_thompson5910 x^3+1 is not odd

Answer 8

1 = 1x^0

Answer 9

so x^3 + 1 is the same as x^3 + 1x^0

we have an odd exponent (3) and an even exponent (0)

Answer 10

I never said f(x) = x^3 + 1 was an odd function