SOLUTION: How do you show if these equations are odd, even, or neither? f(x)=x^3-8x f(x)=3x^4-7x+2 I know looking at the graph how to tell but how do you know what test to perform? And

Algebra ->  Functions -> SOLUTION: How do you show if these equations are odd, even, or neither? f(x)=x^3-8x f(x)=3x^4-7x+2 I know looking at the graph how to tell but how do you know what test to perform? And      Log On


   

Question 1051337: How do you show if these equations are odd, even, or neither?
f(x)=x^3-8x f(x)=3x^4-7x+2
I know looking at the graph how to tell but how do you know what test to perform? And what tests are these?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
ODD function:
f%28-x%29=-f%28x%29

EVEN function:
f%28x%29=f%28-x%29

Some functions are not odd and not even.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
How do you show if these equations are odd, even, or neither?
1. f(x)=x^3-8x
2. f(x)=3x^4-7x+2
~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  f(x) = x^3 - 8x

    To decide if it is odd, even, or neither, we must to consider f(-x) and compare it with f(x).

    f(-x) = (-x)^3 - 8*(-x).

    It is equal to 

    f(-x) = (-x)^3 - 8*(-x) = -x^3 + 8x = -(x^3 -8).

    What is the very right side expression? It is nothing else as -f(x).

    So, we got f(-x) = -f(x).

    It means that the function f(x) is ODD.


2.  If you do the same with the function "N2", you will get that that this function is neither even nor odd.