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

  • Thread starter Thread starter Caldus
  • Start date Start date
  • Tags Tags
    even
Click For Summary
SUMMARY

The function x^3 - x + 1 is classified as neither even nor odd. An even function satisfies the condition f(-x) = f(x), while an odd function meets the requirement f(-x) = -f(x). Upon substituting -x into the function, it does not fulfill either condition. Additionally, the polynomial's symmetry characteristics confirm that it does not exhibit the necessary properties of even or odd functions.

PREREQUISITES
  • Understanding of polynomial functions
  • Knowledge of function symmetry
  • Familiarity with the definitions of even and odd functions
  • Graphing techniques for visual analysis
NEXT STEPS
  • Explore the properties of polynomial functions in detail
  • Learn about function transformations and their effects on symmetry
  • Investigate graphical methods for determining function characteristics
  • Study examples of even and odd functions for comparison
USEFUL FOR

Students studying algebra, mathematicians analyzing function properties, and educators teaching concepts of symmetry in functions.

Caldus
Messages
106
Reaction score
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
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
 
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)
 
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)
 

Similar threads

Undergrad Odd/even functions and fractional indices
  • · Replies 28 ·
Replies
28
Views
5K
High School Odd or Even? -1/x: Origin Symmetric?
  • · Replies 8 ·
Replies
8
Views
3K
MHB Fourier Series involving Hyperbolic Functions
  • · Replies 9 ·
Replies
9
Views
4K
High School Decomposition of a function into even and odd parts
  • · Replies 28 ·
Replies
28
Views
7K
High School Understanding the Odd and Even Nature of sin(x^3)
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Proving Goldbach's conjecture by induction (or why it doesn't seem to work)
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
2K
Odd/Even functions and integration of them
  • · Replies 2 ·
Replies
2
Views
2K
High School Equations vs. Functions Quadratic and Cubic?
  • · Replies 6 ·
Replies
6
Views
2K
High School Behavior of polynomial functions at their zeros
  • · Replies 6 ·
Replies
6
Views
3K