Graphs and Functions

These flashcards cover key concepts related to graphs and functions, including definitions of various types of functions and their properties.

Continuity

A function is continuous over an interval of its domain if its hand-drawn graph can be sketched without lifting the pencil from the paper.

Identity Function

A function defined as f(x) = x, continuous over its entire domain (–∞, ∞).

Squaring Function

A function defined as f(x) = x², continuous on its entire domain (–∞, ∞) and increases on the interval (0, ∞).

Cubing Function

A function defined as f(x) = x³, continuous on its entire domain (–∞, ∞) and increases on its entire domain.

Square Root Function

A function defined as f(x) = √x, continuous on its domain [0, ∞) and increases on its entire domain.

Cube Root Function

A function defined as f(x) = ³√x, continuous on its entire domain (–∞, ∞) and increases on its entire domain.

Absolute Value Function

A function defined as f(x) = |x|, continuous on its entire domain (–∞, ∞), decreases on the interval (–∞, 0) and increases on (0, ∞).

Piecewise-Defined Function

A function composed of multiple segments or pieces, where each piece has its own domain.

Greatest Integer Function

A function defined as f(x) = ⌊x⌋, constant on intervals and discontinuous at all integer values.

Relation x = y²

A relation where the domain is paired with multiple range values, not a function.