Calculus 1 - Week 1.2: Functions and Representations (Vocabulary)

Vocabulary flashcards covering key terms from the Functions unit: domain, range, representations (table, graph, formula), and related concepts.

Function

A relation that assigns exactly one output to each input in its domain; consists of a set of inputs (domain), a set of outputs (range), and a rule.

Domain

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

Range

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

Independent variable

The input variable of a function, typically denoted as x.

Dependent variable

The output variable of a function, typically denoted as y.

Input

The value placed into the function (often x).

Output

The resulting value after applying the function's rule (often f(x) or y).

f(x)

Notation for the function's output corresponding to input x.

Evaluating a function

Finding the output for a given input by substituting into the function, performing operations, and simplifying to obtain f(x) or y.

Table representation

A tabular representation of a function with input-output pairs.

Graph representation

A visual representation of a function on a coordinate plane using points (x, y) where y = f(x).

X-axis

The horizontal axis representing input values (the independent variable).

Y-axis

The vertical axis representing output values (the dependent variable).

Points (x, y) on a graph

Coordinate pairs where y = f(x).

Vertical Line Test

A graph represents a function if no vertical line intersects it more than once.

Plotting from a table

Plot values from a table on a graph to visualize the function.

Formula representation

An explicit function definition, such as y = f(x) = …; used to calculate and graph functions.

Circle area formula

A(r) = πr^2.

Height of an object formula

h(t) = -16t^2 + v0t + h0.

Compound interest formula

A(t) = P(1 + r)^t.

Domain notation

Interval notation or set notation used to describe input constraints (e.g., [a, ∞)).

Range notation

Interval notation or set notation used to describe output constraints.

Restrictions

Conditions to avoid invalid operations (e.g., no division by zero, no negative under even roots).

Relation vs. Function in real life

A relation is a connection between sets; a function assigns exactly one output to each input (e.g., legal name as a function from people to names).