Flashcards: Understanding Relations and Functions — 20 cards

Relations — definition?

Connections between elements of two sets via a rule.

Arrow diagram — purpose?

Visually represents relations with sets and arrows.

Ordered pairs — format?

(x, y), shows relation direction from x to y.

Domain — role?

Set of all possible input values.

Codomain — role?

Set of all potential output values.

Range — difference from codomain?

Actual outputs; subset of the codomain.

Function — key property?

Assigns exactly one output per input.

Input variables — also?

Independent variables, determine the output.

Output variables — also?

Dependent variables, depend on inputs.

Functional relationship — notation?

y = f(x), output as a function of input.

Multivariate functions — involve?

More than one independent variable.

Bivariate functions — involve?

Exactly two independent variables.

Linear functions — shape?

Straight line graph.

Quadratic functions — form?

Second-degree polynomial, parabola shape.

Polynomial functions — example?

Sum of powers of x, e.g., ax^n + ... + a0.

Exponential functions — form?

Variable as an exponent, e.g., a^x.

Logarithmic functions — inverse of?

Exponential functions, f(x) = log_a x.

Relation vs function — difference?

Functions assign one output; relations may assign many.

Directionality in relations?

From domain (input) to codomain (output).

Range — significance?

Set of actual outputs produced by the relation.