Question

Is the function odd, even, or neither? f(x)=x^9-x^4

Answer 1

Welcome to Open Study!!

Answer 2

Do you know how a function can be a odd, even or neither..

Answer 3

Graph it. If the line of symmetry is the y-axis, it is even. If the function symmstrical about the origin, it is odd

Answer 4

Here is a graph of your function
https://www.desmos.com/calculator/0cpxscwgzj

Answer 5

http://www.mathsisfun.com/algebra/functions-odd-even.html

Answer 6

It it doesn't have any symmetry, it is neither

Answer 7

Trick.
Since it is just a polynomial, look at the exponents.
If the exponents are all even. then f is even
If the exponents are all odd, then f is odd
If the exponents are mixtures of even and odds, then it is neither odd or even.
You can apply the actually definitions to see this trick.
f(x)=f(-x) implies f is even
-f(x)=f(-x) implies f is odd