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# Pre-Calculus Definitions

Browse our growing collection of pre-calculus definitions:

#### ARC

ARC an abbreviation of average rate of change is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y…

#### Algorithm

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at …

#### Argand Plane

The argand plane otherwise known as the complex plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis…

#### Average Rate of Change

Average rate of change or ARC is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy)…

#### Bidimensional Space

Bidimensional space otherwise referred to as two dimensional space is a geometric setting in which two values (called parameters) are required to determine the…

#### Box Product

Box product otherwise referred to as scalar triple product, mixed product and triple scalar product is a method of multiplying three 3-dimensional vectors, usu…

#### Complex Plane

The complex plane otherwise known as the argand plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis…

#### Compression

A compression or contraction is a transformation in which a figure grows smaller. Compressions may be with respect to a point (compression of a geometric figur…

#### Delta (Δ, δ)

Delta (Δ, δ) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4.

#### Fixed

Fixed means that the object is regarded as fixed in the plane so that it may not be picked up and flipped if referring to a planar object. As a result, mirror …

#### Greek Alphabet

The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabe…

#### Horizontal Dilation

A horizontal dilation or stretch is a stretch in which a plane figure is distorted horizontally.

#### Horizontal Stretch

A horizontal stretch or dilation is a stretch in which a plane figure is distorted horizontally.

#### Jump Discontinuity

A jump discontinuity or step discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another. It is a disconti…

#### Lemniscate

A lemniscate is a curve usually expressed in polar coordinates and is in the form of any of the various figure eight shaped curves.

#### Mixed Product

Mixed product otherwise referred to as scalar triple product, triple scalar product and box product is a method of multiplying three 3-dimensional vectors, usu…

#### Omega (Ω, ω)

Omega (Ω, ω) is the 24th and last letter of the Greek alphabet. In the system of Greek numerals it has a value of 800.

#### Phi (Φ, φ)

Phi (Φ, φ) is the 21st letter of the Greek alphabet. In the system of traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ).

#### Rho (Ρ, ρ)

Rho (Ρ, ρ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res.

#### Scalar Triple Product

Scalar triple product otherwise referred to as triple scalar product, mixed product and box product is a method of multiplying three 3-dimensional vectors, usu…

#### Sigma (Σ, σ)

Sigma (Σ, σ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ i…

#### Step Discontinuity

A step discontinuity or jump discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another.

#### Tau (Τ, τ)

Tau (Τ, τ) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.

#### Theorem of Pappus

The theorem of Pappus or Pappus's theorem generally refer to several different theorems. They include Pappus's centroid theorem, the Pappus chain, Pa…

#### Triple Scalar Product

Triple scalar product otherwise referred to as scalar triple product, mixed product and box product is a method of multiplying three 3-dimensional vectors, usu…

#### Two Dimensional

Two dimensional or two dimensions is the property of a plane that indicates that motion can take place in two perpendicular directions.

#### Two Dimensional Space

Two dimensional space otherwise referred to as bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine th…

#### Two Dimensions

Two dimensions or two dimensional is the property of a plane that indicates that motion can take place in two perpendicular directions.

#### Unit Vector

A unit vector is a vector with a length or magnitude of 1. Sometimes, the unit vector is also called a direction vector.

#### Vector

Vectors are a quantity, drawn as an arrow, with both direction and magnitude. For example, force and velocity are vectors. If a quantity has a magnitude but no…

#### Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

#### Vertical Compression

A vertical compression or shrink is a compression in which a plane figure is distorted vertically.

#### Vertical Dilation

A vertical dilation or stretch is a stretch in which a plane figure is distorted vertically.

#### Vertical Line Test

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of…

#### Vertical Shift

In geometry, a vertical shift otherwise known as vertical translation, is a translation of a geometric object in a direction parallel to the vertical axis of t…

#### Vertical Shrink

A vertical shrink or compression is a shrink in which a plane figure is distorted vertically.

#### Vertical Stretch

A vertical stretch or dilation is a stretch in which a plane figure is distorted vertically.

#### Vertical Translation

In geometry, a vertical translation otherwise known as vertical shift, is a translation of a geometric object in a direction parallel to the vertical axis of t…

#### Volume

Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm^{3}, in^{3}, m^{3} km^{3}, etc.)

#### X-Y Plane

A plane formed by the x-axis and the y-axis.

#### X-Z Plane

A plane formed by the x-axis and the z-axis.

#### Y-Z Plane

A plane formed by the y-axis and the z-axis.

#### Zero Matrix

A zero matrix is an m x n matrix where all of its elements are equal to zero and denoted by _{0}. Zero matrices are sometimes also referred to as null matrices.

#### Zero Vector

A vector with a magnitude of zero. Denoted 0, it is a vector of length 0, and thus has all components equal to zero.