Functions and Their Graphs: Domain, Range, and Operations

Ten vocabulary flashcards covering core function concepts from the lecture notes.

Function

A relation in which each input value x is assigned a unique output value y; typically written as y = f(x).

Domain

The set of all possible input values (the independent variable) for which the function is defined.

Range

The set of all possible output values (the dependent variable) produced by the function.

Independent variable

The input variable (commonly x) whose values determine the output of the function.

Dependent variable

The output variable (commonly y) whose value depends on the input.

Ordered pair

A pair (x, y) representing an input-output relationship; in a function, each x is paired with a y.

Even function

A function f is even if f(-x) = f(x) for all x in the domain; its graph is symmetric about the y-axis.

Odd function

A function f is odd if f(-x) = -f(x) for all x in the domain; its graph is symmetric about the origin.

Evaluation of a function

Substituting a specific value of x into f(x) to compute the corresponding output f(a).

Composite function

A function formed by applying one function to the result of another, written as (f o g)(x) = f(g(x)).