Is x^3 - x + 1 an Even, Odd, or Neither Function?

  • Thread starter Caldus
  • Start date
  • Tags
    even
In summary, the function x^3 - x + 1 is neither even nor odd. It is not even because it does not satisfy the condition f(-x) = f(x), and it is not odd because it does not satisfy the condition f(-x) = -f(x). Additionally, when graphed, it does not exhibit rotational or vertical symmetry. Therefore, it can be concluded that the function is neither even nor odd.
  • #1
Caldus
106
0
Is the function x^3 - x + 1 even, odd, or neither? When I graphed this, it looked like it was symmetric about the origin, so I thought that it might be an odd function. Either that or it is neither?
 
Mathematics news on Phys.org
  • #2
A function is even if:

f(-x) = f(x)

A function is odd if:

f(-x) = -f(x)

So to figure out if it's even of odd, plug in -x in place of x and compare it to the original.

cookiemonster
 
  • #3
Look at graph

Also I believe that odd fuctions are rotationaly symetric while even fuctions are symetic on the vertical line. (When a graph is fliped horizontally over it)
 
  • #4
f(0) isn' 0 so it certainly isn't odd, and clearly it isn't even.

hint: a polynomial in x is even (odd) iff the powers of x are all even (odd)
 

FAQ: Is x^3 - x + 1 an Even, Odd, or Neither Function?

What is the definition of an even number?

An even number is any integer that can be divided by 2 without leaving a remainder. In other words, an even number is any number that is divisible by 2.

How do you determine if a number is even or odd?

To determine if a number is even or odd, you can divide the number by 2. If the result is a whole number, then the number is even. If the result is a decimal or a fraction, then the number is odd.

What is the difference between even and odd numbers?

The main difference between even and odd numbers is that even numbers can be divided by 2 without leaving a remainder, while odd numbers cannot be divided by 2 without leaving a remainder.

Is zero an even or odd number?

Zero is an even number. This is because it can be divided by 2 without leaving a remainder, and it is the only number that is neither even nor odd.

Can a number be both even and odd?

No, a number cannot be both even and odd at the same time. A number is either even or odd, depending on whether it can be divided by 2 without leaving a remainder or not.

Similar threads

I Odd/even functions and fractional indices
Replies
28
Views
4K
B Odd or Even? -1/x: Origin Symmetric?
Replies
8
Views
2K
MHB Fourier Series involving Hyperbolic Functions
Replies
9
Views
3K
B Decomposition of a function into even and odd parts
Replies
28
Views
6K
B Understanding the Odd and Even Nature of sin(x^3)
Replies
8
Views
3K
Odd/Even functions and integration of them
Replies
2
Views
1K
B Equations vs. Functions Quadratic and Cubic?
Replies
6
Views
2K
B Behavior of polynomial functions at their zeros
Replies
6
Views
2K
Even and Odd functions - Fourier Series
Replies
10
Views
4K
MHB Proving an Odd Function: ln(x+√(1+x²))
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top