Functions Lecture Notes

A set of flashcards summarizing key concepts from the lecture on functions.

Function

A correspondence where each element of one set X results in only one element of another set Y.

Domain

The set of all permitted values of x for which a corresponding y value exists in a function.

Range

The set of all resulting values of y from the permitted values of x in a function.

Independent Variable

The variable x in a function, which can take on any value from the domain.

Dependent Variable

The variable y in a function, which depends on the value of the independent variable x.

Relation

Any correspondence of a set X to a set Y without the restriction that each element in X maps to only one in Y.

Polynomial Function

A function that can be expressed in the form f(x) = anxn + an-1xn-1 + … + a1x + a0, where a0, a1, a2, …, an are real numbers.

Rational Function

A function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials.

Radical Function

A function that can be expressed in the form f(x) = $ext{√} g(x)$, where g(x) is a polynomial.

Limit of a Function

The value that a function approaches as the input approaches a certain point.