Calculus Terms

Function

A relation in which each input in the domain has one and only one output.

Increasing Function

A function in which the value of the output (the y value) increases as the input value (the x value) increases.

Decreasing Function

A function in which the value of the output (the y value) increases as the input value (the x value) increases

Even Function

A function f(x) in which all values of x in the domain f(x) = f(-x); equivalently, the graph of f(x) is symmetric with respect to the y-axis.

Odd Function

A function f(x) in which all values of x in the domain f(x) = -f(-x); equivalently, the graph of f(x) is symmetric with respect to the x-axis.

Bounded Function

A function f(x) is bounded if f(x) is less than or equal to a constant |f(x)| <= M for all values of x in the domain.

Unbounded Function

A function f(x) is unbounded if a constant M such that |f(x)| <= M does not exist for all values of x.

Vector

A mathematical structure that has both magnitude and direction, represented by an ordered pair of components.

Magnitude Of A Vector

The length of a vector, denoted by || ||.

Direction Of A Vector

The counter-clockwise angle from the positive x-axis to the vector.

Unit Vector

Vector with magnitude 1.

Parametric Equation

A set of equations describing relations between variables using parameters.

Polar Coordinate

A point represented in terms of its distance from the origin and angle from the x-axis.

Cartesian/Rectangular Coordinate

A point represented in terms of its distance from the x-axis and y-axis.