Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:Physics
Economics Engineering Computer science |
| gptkbp:basisFor |
Monomials
Standard basis |
| gptkbp:coefficient |
a_n
|
| gptkbp:definedIn |
Functions that can be represented by a polynomial expression
|
| gptkbp:degree |
n
|
| gptkbp:designer |
Not always a polynomial
|
| gptkbp:domain |
gptkb:Complex_numbers
Real numbers |
| gptkbp:expressionForm |
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0
|
| gptkbp:field |
gptkb:Mathematics
gptkb:algebra |
| gptkbp:fundamentalTheorem |
gptkb:Fundamental_Theorem_of_Algebra
|
| gptkbp:generalizes |
Rational functions
Power series |
| gptkbp:graphFeature |
End behavior determined by leading term
Intercepts Turning points |
| gptkbp:hasSpecialCase |
gptkb:Quadratic_function
Cubic function Linear function Constant function |
| https://www.w3.org/2000/01/rdf-schema#label |
Polynomial functions
|
| gptkbp:notation |
P(x)
f(x) g(x) |
| gptkbp:operator |
Addition
Multiplication Subtraction Division (with remainder) |
| gptkbp:property |
Smooth
Closed under addition Closed under multiplication Closed under scalar multiplication Continuous everywhere Differentiable everywhere |
| gptkbp:range |
gptkb:Complex_numbers
Real numbers |
| gptkbp:rootWord |
Value of x where f(x)=0
|
| gptkbp:shape |
Smooth curve
|
| gptkbp:usedIn |
Numerical analysis
Approximation theory Interpolation |
| gptkbp:variant |
x
|
| gptkbp:zero |
Root
|
| gptkbp:bfsParent |
gptkb:Entire_Functions
|
| gptkbp:bfsLayer |
7
|