# ALGEBRA GLOSSARY

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Title Description
Decreasing Decreasing means to lessen in extent or scope, to be reduced.
A function is considered to be Decreasing if the values in the range decrease as the values from the domain increase.
Deductive Logic Deductive Logic is employed before events have transpired, before the fact.
Degree, Polynomial The Degree of a polynomial is the order, or highest power (term) of the polynomial.
Delta Delta is the fourth letter of the Greek alphabet.
Upper-case Delta looks like a triangle and is used to mean "the change in..."
Denominator The Denominator of a fraction is the number on the bottom; it is the divisor of the numerator.
Dependent Variable If y = f(x), then y is a function of x and y is the Dependent Variable.
Think of it this way: whatever we get for output "y" depends on the input "x" we grab from the domain of the function.
Determinant A Determinant is a number associated with a square matrix.
It may also be a cofactor, a number associated with a square array from a larger matrix.
Diagonal Matrix A square matrix with zero values everywhere except on the main diagonal (upper left to lower right) is termed a Diagonal Matrix.
Dimension, Matrix The Dimension of a matrix is its order, or size.
We label the order of a matrix by its number of rows then its number of columns.
A 4x3 matrix is read as "a four by three matrix" and has four rows and three columns.
Direct Proportion When variables are in Direct Proportion to one another they have the relation that as one variable grows the other either increases or decreases by a constant multiplication factor.
When y = kx, we say the variables are in Direct Proportion.
Direct Variation Also direct proportion, Direct Variation describes the relation y = kx.
Discontinuity When a function is literally not continuous because of a gap, a step, a hole, or any kind of "break" it is considered discontinuous.
Discrete Function When the inputs from the domain of the function are not smooth and continuous but rather incremental, the function is considered to be a Discrete Function.
In general, a Discriminant provides algebraic information about the roots of polynomials.
Disjoint Disjoint sets have no common elements.
Distance Formula The familiar Distance Formula in Cartesian (rectangular) coordinates is a version of the Pythagorean Theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Distributive Property The familiar Distance Formula in Cartesian (rectangular) coordinates is a version of the Pythagorean Theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Divergent Geometric Progression An infinite geometric progression (or a significant portion of one) is termed Divergent when its common ratio has an absolute value less than or equal to -1, or greater than or equal to 1.
Domain The values that are "legal" and "legitimate" to put into a function are the elements of the Domain of that function.
When y = f(x), the legitimate values of x are the Domain of the function.
Dot Product A product of vector multiplication, the Dot Product is a scalar, which means it has magnitude only and not an associated direction.
The Dot Product does not result in another vector.
Doubling Time The time it takes an exponential or geometric growth to double in size (grow by 100 percent of the original value) is its doubling time.

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