Algebra 1: Relations, Functions, and Graphs

Vocabulary practice flashcards covering relations, functions, domain and range, linearity, continuity, intercepts, and graphical features.

Relation

A set of ordered pairs containing input values ($x$) and output values ($y$) that can be represented as a table, a graph, or a mapping diagram.

Domain

The set of all possible input values or $x$-coordinates in a relation, denoted as $D$.

Range

The set of all possible output values or $y$-coordinates in a relation, denoted as $R$.

Mapping Diagram

A representation of a relation consisting of two parallel sets with directed arrows showing pairings from elements in the domain to elements in the range.

Independent Variable

The variable in a relation that determines the output value; graphed along the horizontal axis ($x$-axis).

Dependent Variable

The variable in a relation whose value depends on the independent variable; graphed along the vertical axis ($y$-axis).

Scale

The quantitative value or measurement increment represented by each grid unit or mark on a coordinate axis.

Origin

The coordinate point $(0, 0)$ where the $x$-axis and $y$-axis intersect, representing a starting value of zero for both variables.

Function

A specific type of relation in which each element of the domain is paired with exactly one unique element of the range.

Vertical Line Test

A visual test to determine whether a graph represents a function; if a vertical line passes through more than one point anywhere on the graph, the relation is not a function.

Continuous Function

A function that is graphed with a single unbroken curve or line with no gaps, holes, or breaks.

Discrete Function

A function whose graph is made up entirely of distinct, isolated, individual points.

Neither Continuous nor Discrete Function

A function that features continuous sections or segments but does not form a single unbroken line or curve.

Linear Function

A function that has a constant rate of change and graphs as a single straight line.

Nonlinear Function

A function whose rate of change is not constant, resulting in a graph that is not a straight line.

$x$-intercept

The coordinate point where a graph intersects the $x$-axis, corresponding to an output value of $y = 0$.

$y$-intercept

The coordinate point where a graph intersects the $y$-axis, corresponding to an input value of $x = 0$.

Zero of a Function

The input value $x$ for which the function's value is zero ($f(x) = 0$), which corresponds directly to the $x$-intercept.

Positive Function Interval

The interval along the $x$-axis where the graph lies above the horizontal axis ($y > 0$).

Negative Function Interval

The interval along the $x$-axis where the graph lies below the horizontal axis ($y < 0$).

Increasing Function

A section of a graph where the $y$-values increase as the $x$-values move from left to right.

Decreasing Function

A section of a graph where the $y$-values decrease as the $x$-values move from left to right.

Relative Maximum

A point on a graph where a function transitions from increasing to decreasing, forming a local peak.

Relative Minimum

A point on a graph where a function transitions from decreasing to increasing, forming a local trough or low point.

End Behavior

A description of the values and trajectory of $y$ as the independent variable $x$ moves toward positive or negative infinity.