Algebra: Relations, Functions, and Arithmetic Sequences

Vocabulary flashcards covering foundational algebra concepts including relations, functions, domain, range, function notation, zeros, and arithmetic sequences.

Relation

A set of ordered pairs.

Domain

The set of first numbers ($x$-values) of the ordered pairs in a relation.

Range

The set of second numbers ($y$-values) of the ordered pairs in a relation.

Mapping

A visual representation that illustrates how each element of the domain is paired with an element of the range.

Function

A relation in which each element of the domain is paired with exactly one element of the range (where $x$-values do not repeat).

Function Notation

A way to name a function that is defined by an equation by replacing "$y$" with "$f(x)$".

Input

A value substituted for an $x$-value in a function.

Output

The result of substituting a value into a function.

Vertical Line Test

A visual test stating that if any vertical line passes through the graph of a relation no more than once, then it is a function.

Zeros

The $x$-intercepts of the graph of a function, representing the points for which $f(x) = 0$.

Arithmetic Sequence

A numerical pattern that increases or decreases at a constant rate or value.

Common Difference ($d$)

The difference between consecutive terms in an arithmetic sequence.

Arithmetic Sequence Formula

A formula used to find the $n^{\text{th}}$-term of an arithmetic sequence: $a_n = a + d(n - 1)$.