algebraic function: meaning, definition, pronunciation and examples
C1/C2Academic / Technical
Quick answer
What does “algebraic function” mean?
A mathematical function defined using a finite combination of algebraic operations: addition, subtraction, multiplication, division, and raising to a rational power.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function defined using a finite combination of algebraic operations: addition, subtraction, multiplication, division, and raising to a rational power.
In a broader sense, any function expressible as a root of a polynomial equation whose coefficients are themselves polynomials.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of related terms may follow national conventions (e.g., BrE 'formulae' vs. AmE 'formulas').
Connotations
None. Purely technical term.
Frequency
Equally frequent in both varieties within technical contexts; extremely rare in general discourse.
Grammar
How to Use “algebraic function” in a Sentence
[algebraic function] of [variable]an [adjective] algebraic function[verb] an algebraic functionVocabulary
Collocations
Examples
Examples of “algebraic function” in a Sentence
verb
British English
- We need to algebraicise the relationship before solving.
American English
- We need to algebraize the relationship before solving.
adverb
British English
- The expression was manipulated algebraically.
American English
- The expression was manipulated algebraically.
adjective
British English
- The solution took an algebraic form.
American English
- The solution took an algebraic form.
Usage
Meaning in Context
Business
Almost never used.
Academic
Core term in undergraduate and postgraduate mathematics, physics, and engineering courses.
Everyday
Virtually never used.
Technical
Essential term in mathematical analysis, algebraic geometry, and control theory.
Vocabulary
Synonyms of “algebraic function”
Neutral
Weak
Vocabulary
Antonyms of “algebraic function”
Watch out
Common Mistakes When Using “algebraic function”
- Incorrectly classifying functions like sin(x) or e^x as algebraic. Mispronouncing 'algebraic' (stress on 'bre' / 'breɪ/', not on 'al'). Using it as a general synonym for 'mathematical function'.
FAQ
Frequently Asked Questions
Yes. Polynomials are a fundamental subclass of algebraic functions.
Yes. Functions involving roots (with rational exponents) are algebraic, e.g., f(x) = √x or f(x) = ⁵√(x³+1).
An algebraic function can be defined by a polynomial equation, while a transcendental function (like sin, cos, exp, log) cannot.
No. The domain can be restricted, for example, by even roots of negative numbers or division by zero.
A mathematical function defined using a finite combination of algebraic operations: addition, subtraction, multiplication, division, and raising to a rational power.
Algebraic function is usually academic / technical in register.
Algebraic function: in British English it is pronounced /ˌæl.dʒɪˌbreɪ.ɪk ˈfʌŋk.ʃən/, and in American English it is pronounced /ˌæl.dʒəˌbreɪ.ɪk ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think 'Algebra I See' – the function uses only operations you first learn in basic algebra (add, subtract, multiply, divide, powers).
Conceptual Metaphor
A RECIPE using only basic kitchen operations (combine, separate, replicate, portion, intensify).
Practice
Quiz
Which of the following is an algebraic function?