Graphs: Domain, Range, Functions, and Equation Restrictions

Vocabulary flashcards covering key terms from the lecture notes about domain, range, the function concept, the vertical line test, and restrictions when solving fractions and radicals.

Domain

The set of all x-values for which a graph or relation has points; the inputs to the function.

Range

The set of all y-values produced by a graph or relation; the outputs of the function.

Coordinate Points

Pairs (x, y) that lie on a graph, representing input-output values for the relation.

Vertical Line Test

A test to determine if a graph represents a function by checking that no vertical line intersects the graph more than once.

Function

A relation where each x-value maps to exactly one y-value; repeated x-values with different y-values mean it is not a function.

Undefined

A value or expression that has no meaning in the real numbers, commonly arising from division by zero.

Denominator

The bottom part of a fraction; it cannot be zero. To find restrictions, set the denominator equal to zero and solve for x.

Radical with Even Index

A root where the index is even (e.g., square root); the radicand inside must be nonnegative to be real.

Restriction

A condition that excludes certain x-values from the domain to keep expressions defined (e.g., where the denominator is zero or a radical would be invalid).

Isolating the Variable

The process of rearranging an equation to get the variable of interest by itself on one side, often by dividing both sides when the coefficient is not 1.