algebraic function

mathematics

Also known as: algebraic expression

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June 18, 2026

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An algebraic function is a function defined by an algebraic equation. In mathematics, a function establishes a relationship between a dependent variable and one or more independent variables. This relationship is expressed through a rule or formula.12

Algebraic functions are a subset of these functions where the relationship can be described by an algebraic equation. This means the variables in the function are related through operations like addition, subtraction, multiplication, division, and raising to a power. For example, the area of a circle, (A = \pi r^2), is a polynomial function, which is a type of algebraic function. In contrast, transcendental functions, like exponential or trigonometric functions, cannot be expressed solely through algebraic equations.123

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elementary algebra
Algebraic expressions
Any of the quantities mentioned so far may be combined in expressions according to the usual arithmetic operations of addition, subtraction, and multiplication. Thus, ax + by and axx + bx + c are common algebraic expressions. However, exponential notation is commonly used…
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Any of the quantities mentioned so far may be combined in expressions according to the usual arithmetic operations of addition, subtraction, and multiplication. Thus, ax + by and axx + bx + c are common algebraic expressions. However, exponential notation is commonly used…
Read More

function
Common functions
…result is known as an algebraic function.) Polynomial functions have been studied since the earliest times because of their versatility—practically any relationship involving real numbers can be closely approximated by a polynomial function. Polynomial functions are characterized by the highest power of the independent variable. Special names are commonly used…
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…result is known as an algebraic function.) Polynomial functions have been studied since the earliest times because of their versatility—practically any relationship involving real numbers can be closely approximated by a polynomial function. Polynomial functions are characterized by the highest power of the independent variable. Special names are commonly used…
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mathematics
Algebraic topology
He had studied algebraic functions—that is, loci defined by equations of the form f(x, y) = 0, where f is a polynomial in x whose coefficients are polynomials in y. When x and y are complex variables, the locus can be thought of as a real surface spread…
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He had studied algebraic functions—that is, loci defined by equations of the form f(x, y) = 0, where f is a polynomial in x whose coefficients are polynomials in y. When x and y are complex variables, the locus can be thought of as a real surface spread…
Read More