Can absolute value functions be considered polynomial functions?

Click For Summary
SUMMARY

Absolute value functions, such as |x|^3, are not classified as polynomial functions. This conclusion is based on the definition of polynomials, which require the absence of absolute value operations. Additionally, every cubic polynomial function, defined as a function from R to R, has a codomain that encompasses all real numbers, meaning there are no cubic polynomials that fail to cover this range.

PREREQUISITES
  • Understanding of polynomial function definitions
  • Knowledge of absolute value functions
  • Familiarity with cubic functions and their properties
  • Basic concepts of real number ranges and codomains
NEXT STEPS
  • Research the definition and properties of polynomial functions
  • Explore the characteristics of absolute value functions
  • Study the range and codomain of cubic functions
  • Investigate examples of non-polynomial functions
USEFUL FOR

Mathematics students, educators, and anyone interested in understanding the distinctions between polynomial and absolute value functions.

LordCalculus
Messages
12
Reaction score
0
Are lx3l or lxl3 polynomials?

If not, what would be a good example of a cubic polynomial function (R \rightarrow R) that doesn't cover all real numbers in its codomain?
 
Mathematics news on Phys.org
Answer to your first question- no, they are not polynomials.

Answer to your second question, there is none. Every cubic polynomial has range all real numbers.
 

Similar threads

Undergrad What type is a polynomial function?
  • · Replies 7 ·
Replies
7
Views
2K
High School Confusion about The Conjugate Roots Theorem
  • · Replies 8 ·
Replies
8
Views
2K
MHB Understanding Cubic Equation Formula for Polynomials of Degree Three
  • · Replies 9 ·
Replies
9
Views
4K
High School General explicit solution to polynomial interpolation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How Does Gaussian-Legendre Quadrature Approximate Non-Polynomial Functions?
  • · Replies 2 ·
Replies
2
Views
2K
High School Definition of a polynomial? and degree? integral and ration
  • · Replies 11 ·
Replies
11
Views
2K
High School Understanding Horner's Method: A Brief Explanation for Confusion
  • · Replies 7 ·
Replies
7
Views
3K
High School Notation for a "scalar absolute field"?
  • · Replies 1 ·
Replies
1
Views
2K
High School Upper and Lower Bounds of Polynomials
  • · Replies 8 ·
Replies
8
Views
5K
Graduate Is there a strictly algebraic way of coding "whole number value of"?
  • · Replies 8 ·
Replies
8
Views
2K